Geometric Series Word Problems Pdf


Here are a set of practice problems for the Calculus II notes. The patient is told to walk a distance of 5 km the first week, 8 km the second week, 11 km the third week and so on for a period of 10 weeks. 2 The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve real-world problems, including writing the first n terms, finding the nth term, and. Determine the values of 2R for which P 1 n=1 n +1 n converges. Get Started. However, our rules of probability allow us to also study random variables that have a countable [but possibly infinite] number of possible values. Geometric Sequences. An arithmetic series is essentially the sum of the terms contained in an arithmetic sequence. 40, 43, 46, 49, 52. I have an arithmetic progression such that the initial term is 5 and the common difference is 10. 9) a 1 = −1, r = −2 Find a 11 10) a 1 = −4, r = 3. Worksheets are Geometric sequences date period, 9 11 sequences word, , Work 3 6 arithmetic and geometric progressions, Arithmetic and geometric sequences and series expressions, Suites et sries gomtriquesang, Arithmetic sequences date period, Sequences series work. Determine the general term for the sequence. For this series, nd (a) the common ratio, [2] (b) the rst term, [2] (c) the sum of the rst 50 terms, giving your answer to 3 decimal places, [2]. Solve the problem. If the second differences in a sequence are constant, a cubic function best models the sequence. , a, ar, ar2, , arn - 1, Here, common ratio r = -1. A progression (a n) ∞ n=1 is told to be geometric if and only if exists such q є R real number; q ≠ 1, that for each n є N stands a n+1 = a n. 2 Geometric Series probability practice and intro to geometric series Def of geometric, sum formulas, when converges 9. Worksheet on Geometric Series 1. Geometric Series Problem 1 The large outer square has side length 1. Algebra 2/Trig: Chapter 6 – Sequences and Series In this unit, we will… Identify an arithmetic or geometric sequence and find the formula for its nth term Determine the common difference in an arithmetic sequence Determine the common ratio in a geometric sequence. This series is so special because it will enable us to find such things as Power Series and Power Functions in Calculus!. ½ – 1 + 2 – 4 + … b. Given the first term and the common ratio of a geometric sequence find the first five terms and the explicit formula. If r = −1 this is the sequence of example 11. As with the previous series, as we keep adding terms, the result will get larger. Improve your math knowledge with free questions in "Geometric sequences with fractions" and thousands of other math skills. Khan Academy is a 501(c)(3) nonprofit organization. The formulas for the sum of first numbers are. We tried to locate some good of Geometric Sequences and Series Worksheet Answers and Arithmetic Sequence Word Problems Worksheet with Answers Luxury image to suit your needs. In 2013, the number of students in a small school is 284. After im reading this Arithmetic And Geometric Sequences Ib Hl Problems PDF Download it is very interesting. Geometric Mean Definition. If arithmetic, state the Given a term m an arithmetic sequence and the common difference, find the first term and the 5th term. 1 SEQUENCES SUGGESTED TIME AND EMPHASIS 1 class Essential material After the students have warmed up by doing one or two of the problems as a class, have them start working The analysis and applications of geometric series. Objectives Find the common ratio of a geometric sequence. Find the sum of the n terms of the arithmetic series: 10 2. 25 Arithmetic Sequence Word Problems Worksheet with Answers. Word problems on ages. 53MB GEOMETRIC SERIES WORD PROBLEMS WITH ANSWERS As Pdf, SERIES ANSWERS GEOMETRIC WORD PROBLEMS WITH As Docx, GEOMETRIC ANSWERS WITH SERIES PROBLEMS WORD As Pptx GEOMETRIC SERIES WORD PROBLEMS WITH ANSWERS How easy reading concept can improve to be an effective person? GEOMETRIC SERIES WORD PROBLEMS WITH ANSWERS review is a very simple task. Powered by Create your own unique website with customizable templates. Download File PDF Arithmetic Word Problems With Solutions Math Help Fast (from someone who can actually explain it) See the real life story of how a cartoon dude got the better of math Arithmetic Sequences and Geometric Series - Word Problems This. You're a much better golfer than your friend and anticipate winning all 18. Lacking resources, I created these Guided Notes to introduce the explicit formulas for Arithmetic and Geometric Sequences. The main thing to remember about word problems with sequences and series is that when we want an amount for a single thing, such as a particular row, year, for example, we use a sequence. We can write a formula for the n th term of a geometric sequence in the form a n = a r n , where r is the common ratio between successive terms. OK, so I have to admit that this is sort of a play on words since each element in a sequence is called a term, and we'll talk about the terms (meaning words) that are used with sequences and series, and the notation. When the general term is found, then one can find any term in the sequence without writing all the preceding terms. Does the series P 1 n=1 a n converge or diverge? Prove your claim. Use the formula for the sum of the first terms of a geometric sequence. notebookFebruary 13, 2018 Learning Intention: Students will be solving real life application problems involving Arithmetic and Geometric Sequences. To find a common ratio in a geometric sequence, multiply any term by the previous term. A geometric series is a series or summation that sums the terms of a geometric sequence. The measure of a regular polygon's interior angle is four times bigger than the measure of its external angle. and the three terms in the sequence after the last one given. 5% annual percentage rate, compounded monthly for. Find the sum of the arithmetic series 17 + 27 + 37 ++ 417. Determine the general term for the sequence. 3, 6, 12, 24, 48, … Write an equation for this arithmetic sequence and find the. If a square has an area of 49 ft2, what is the length of one of its sides? The perimeter? how long must its length be. You bet $1 for hole 1 with a "double or nothing" stipulation for each subsequent hole. For example, what is the sum of PDF Pass Chapter 10 24 Glencoe Algebra 2 10-3 Enrichment Half the Distance. Use the formula for the sum of an infinite geometric series. Given the sequence defined by the function 𝑛+1= 3 4 𝑛 with 1=424. 17) a 1 = −4, r = 6 18) a 1. a=5, Find the first 4 terms of the geometric sequence with a=-6 and r= -2/3. Sequences and Series Terms. Sequence; Arithmetic sequence; Geometric sequence. A an = 3 ⋅ (−3)n − 1; 243 C a n = 3 ⋅ (3)n; 243 B an = −3 ⋅ (3)n − 1; -243 D a n = 3 ⋅ (−3)n; -729 ____ 11 You are buying a car for $8,500. Write a formula for the student population. ©l V2D0z1 L29 BKxurt yaF IS 1okf7tSwQaMroe x MLqL 1C t. Sequence And Series Geometric Series Arithmetic Map Activities Word Problems Worksheets Writing Math Words This set of arithmetic sequence worksheets covers the topic like finding the first term, common difference and number of terms; writing general term of an arithmetic sequence, finding the specific term and more!. 5) Σ k = 1 7 4k − 1 5461 6) Σ i = 1 8. Show Step-by-step Solutions Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions. Finite geometric series word problem: mortgage Our mission is to provide a free, world-class education to anyone, anywhere. This section contains basic problems based on the notions of arithmetic and geometric progressions. There are examples, "You-Dos" (student practice problems), and word problems as wel. Finite geometric series word problem: mortgage Our mission is to provide a free, world-class education to anyone, anywhere. Make sure you hit all the problems listed in this page. If rule based, write down the next value in the sequence. There are methods and formulas we can use to find the value of a geometric series. This is a geometric sequence with first terma 5 2, and common ratio quence is the common ratio: given by r 5 a n11 a n 5 2n11 2n 52. A tricky geometry word problem Word problem #5: The midpoint of a segment is (3, 6). PROBLEM: SITUATION: A writer wrote 890 words on the first day, 760 words on the second day and 630 words on the third day, and so on in an arithmetic sequence. Length word problems (metric) Grade 4 Word Problems Worksheets Read and answer each question: 1. Starting with an example, we will head into the problems to solve. But 20% is equivalent to 0. Each page includes appropriate definitions and formulas followed by solved problems listed in order of increasing difficulty. Arithmetic and Geometric Sequences and Series Reporting Category Expressions and Operations Topic Exploring sequences and series Primary SOL AII. Pascal's Triangle. 4 Infinite Geometric Series 675 Infinite Geometric Series USING INFINITE GEOMETRIC SERIES Consider the following infinite geometric series: + 1 2 + 1 4 + 1 8 + 1 1 6 3 1 2 +. Determine the values of 2R for which P 1 n=1 n +1 n converges. In an arithmetic sequence, the differences between consecutive terms are constant. Write an explicit function rule. The president and treasurer each contact three members (round 1), each of whom contact three more members (round 2), each of whom contacts three more members (round 3), etc. mathworksheets4kids. 9) a 1 = −1, r = −2 Find a 11 10) a 1 = −4, r = 3. Telescoping Series Examples Examples 11. Geometric Sequences and Series Worksheet Answers Along with Best Arithmetic and Geometric Sequences Worksheet Awesome 113. LEADING TO applying the properties of geometric sequences and series to functions. A geometric series is a series of the form S = a+ar +ar2 +ar3 +ar4 + : Here the rst term is a and we obtain each of the other terms by multiplying the term preceding it by the ratio r. Download File PDF Arithmetic Word Problems With Solutions Math Help Fast (from someone who can actually explain it) See the real life story of how a cartoon dude got the better of math Arithmetic Sequences and Geometric Series - Word Problems This. 7 and diverges. 25 thousand dollars will be withdrawn this year, and subsequent withdrawals will rise by 1% each year. The nth sum of a series is given by the formula S n = 1 - 4n. Arithmetic Word Problems - Sample Math Practice Problems The math problems below can be generated by MathScore. mathworksheets4kids. 25 + … Evaluate the infinite geometric series, if possible. Knowledge of relevant formulae is a prerequisite to evaluate the sum of an arithmetic series and determine the number of terms. This Finite Geometric Series Worksheet is suitable for 9th - 12th Grade. Word problems on average speed Word problems on sum of the angles of a triangle is 180 degree. In general, in order to specify an infinite series, you need to specify an infinite number of terms. The sequence 16 ,8 ,4 ,2 ,1 ,1/2 ,… = is a decreasing geometric sequence of common ratio ½. √ Arithmetic Sequence Word Problems Worksheet with Answers. A an = 3 ⋅ (−3)n − 1; 243 C a n = 3 ⋅ (3)n; 243 B an = −3 ⋅ (3)n − 1; -243 D a n = 3 ⋅ (−3)n; -729 ____ 11 You are buying a car for $8,500. The problem wants to know TOTAL income after 31 days. Given the first term and the common ratio of a geometric sequence find the first five terms and the explicit formula. Geometric Sequence Word Problem. 17) a 1 = −4, r = 6 18) a 1. A withdrawal will be made once a year. PROBLEM: How many words did the writer write in a week? SOLUTION: The sequence is 890, 760, 630 …. In an arithmetic sequence, the differences between consecutive terms are constant. d) By considering the infinite geometric series formed by the area of the small triangles, find an expression for the total area, in terms of a , b and c. Find the eighth term of a geometric sequence for which 1=−3 and =−2. Times table shortcuts. HW #17 Answers - 2/23: File Size: 84 kb: File Type: pdf: Download File. 8 , r = −5 16) a 1 = 1, r = 2 Given the first term and the common ratio of a geometric sequence find the recursive formula and the three terms in the sequence after the last one given. According to the problem conditions, the sequence of the numbers of seats in the concert hall rows is the arithmetic progression with the first term , Word problems on arithmetic progressions (this lesson) Mathematical induction for sequences other than arithmetic or geometric. com, a math practice program for schools and individual families. The first one has a scale factor 1 and common ratio = 2. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1)=f(n)+f(n-1) for n ≥ 1. Solving Annuity Problems At the beginning of the section, we looked at a problem in which a couple invested a set amount of money each month into a college fund for six years. A simple example is the geometric series for a = 1 and r = 1/2, or 1 + 1/2 + 1/4 + 1/8 +⋯, which converges to a sum of 2 (or 1 if the first term is excluded). a Worksheet by Kuta Software LLC. OK, so I have to admit that this is sort of a play on words since each element in a sequence is called a term, and we'll talk about the terms (meaning words) that are used with sequences and series, and the notation. pdf: Download File. Part 2: Geometric Sequences Consider the sequence $2, 4, 8, 16, 32, 64, \ldots$. 3 Geometric Sequences and Series 973 Figure 10. A sequence of numbers \(\left\{ {{a_n}} \right\}\) is called a geometric sequence if the quotient of successive terms is a constant, called the common ratio. Get high school students to solve this exclusive collection of printable worksheets on arithmetic series. 470 #11, 13-20 p. If an eruption lasts for 2 minutes then the. Arithmetic Sequences and Geometric Sequences This algebra 1 and 2 video provides an overview of arithmetic sequence geometric series. How many sides does the polygon have?. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For this series, nd (a) the common ratio, [2] (b) the rst term, [2] (c) the sum of the rst 50 terms, giving your answer to 3 decimal places, [2]. Some problems are presented in sigma notation, while others are just given the beginning of the series so students mus. This lesson covers finding the sum of a geometric series using the formula and the calculator. For a 10 5 1024. 3250 by paying Rs. A note about the geometric series Before we get into today's primary topic, I have to clear up a little detail about the geometric series. Starting with an example, we will head into the problems to solve. SEQUENCE AND SERIES 149 9. In either case, the sequence of probabilities is a geometric sequence. Concept 16: Arithmetic & Geometric Sequences Assessment (Level 4 Example Question Level 3 Example Question Level 2 Example Question Write an equation for this geometric sequence and find the 10th term of the sequence. With the adoption of the Common Core curriculum, a new topic added to Algebra 2 is sequences. HW #17 - Word Problems 2/23: File Size: 24 kb: File Type: docx: Download File. A withdrawal will be made once a year. They ask you to compute a related quantity or to combine the quantities. Share practice link. 470 #11, 13-20 p. In an arithmetic sequence, the differences between consecutive terms are constant. 588) • geometric series(p. So we need the formula for a geometric series. P1: FXS/ABE P2: FXS 9780521740517c09. Math Busters Word Problems reproducible worksheets are designed to help teachers, parents, and tutors use the books from the Math Busters Word Problems series. The primary difference between arithmetic and geometric sequence is that a sequence can be arithmetic, when there is a common difference between successive terms, indicated by 'd',. There are many applications of sequences. Identify whether the pattern is arithmetic or geometric. 6) A geometric series has a sum of 1365. Let us consider a G. All final solutions MUST use the formula. This problems relates to the nite geometric series S= a+ ar+ ar2 + + arn: (There are n+1 terms. Khan Academy is a 501(c)(3) nonprofit organization. You will need to determine if the series is arithmetic or geometric. Consider, if x 1, x 2 …. a=5, Find the first 4 terms of the geometric sequence with a=-6 and r= -2/3. BF Using a constant ratio to find missing terms in a geometric sequence (F Construct and compare linear, quadratic and exponential models and solve problems. Sequences and Series IB Problems Worksheet 1. 1, 2, 6, 24, 120,. Page 1 of 2 11. Geometric Sequence and Series Word Problems When solving geometric sequence and series word problems you need to follow these steps. question 1 of 3. He usually starts out the semester with only 10 questions on the first exam, but for each subsequent exam he writes one and a half as many questions as were on the previous exam!. You're a much better golfer than your friend and anticipate winning all 18. 25 + … Evaluate the infinite geometric series, if possible. 5 shows a partial graph of the first geometric sequence in our list. How many sides does the polygon have?. The AP Calculus Problem Book Publication history: First edition, 2002 Second edition, 2003 Third edition, 2004 Third edition Revised and Corrected, 2005 Fourth edition, 2006, Edited by Amy Lanchester Fourth edition Revised and Corrected, 2007 Fourth edition, Corrected, 2008 This book was produced directly from the author's LATEX files. When I think of a geometric sequence, I think of something where the initial input value = 1, not 0. Find the sum of the n terms of the arithmetic series: 10 2. One series involves the ball falling, while the other series involves the ball rebounding. Find the scale factor and the command ratio of a geometric progression if. Distinguish between situations that can be modeled with linear functions and with. M) of a series containing n observations is the nth root of the product of the values. The ball will travel approximately 168 inches before it finally comes to rest. De nition 1. the second decidion is -16, 1/2. The fixed number multiplied is referred to as "r". 15) a 1 = 0. 1 SEQUENCES SUGGESTED TIME AND EMPHASIS 1 class Essential material After the students have warmed up by doing one or two of the problems as a class, have them start working The analysis and applications of geometric series. Exercises. The company gave him a starting salary of ₹60,000 and agreed to increase his salary 5% annually. Example 7: Solving Application Problems with Geometric Sequences. There are methods and formulas we can use to find the value of a geometric series. question 1 of 3. Solving Annuity Problems At the beginning of the section, we looked at a problem in which a couple invested a set amount of money each month into a college fund for six years. If one endpoint is (4, 7), what is the other endpoint? Suppose x 1 is the missing x-coordinate of the other endpoint. A geometric sequence is created by repeatedly multiplying an initial number by a constant. Time, speed and distance shortcuts. I recommend reading this Arithmetic And Geometric Sequences Ib Hl Problems Kindle because this. mar 12, 2017 - arithmetic and geometric sequence word problem examples Stay safe and healthy. Worksheets are Geometric sequences date period, 9 11 sequences word, , Work 3 6 arithmetic and geometric progressions, Arithmetic and geometric sequences and series expressions, Suites et sries gomtriquesang, Arithmetic sequences date period, Sequences series work. The president and treasurer each contact three members (round 1), each of whom contact three more members (round 2), each of whom contacts three more members (round 3), etc. How many sides does the polygon have?. The Geometric Mean (G. 1, 2, 6, 24, 120,. c) Find the value of the 15 th term. With the adoption of the Common Core curriculum, a new topic added to Algebra 2 is sequences. Students should have the sequence right before they start the work. 3 Geometric Sequences and Series 667 Finding the nth Term Given a Term and the Common Ratio One term of a geometric sequence is a 3= 5. The 1560 members of the Great Pumpkin Society have a method of quickly notifying members. 999 999 97 ×!10!" 5) a)!=10 b)! =110 6)!!=1. This is a geometric sequence with first terma 5 2, and common ratio quence is the common ratio: given by r 5 a n11 a n 5 2n11 2n 52. 3, 6, 12, 24, 48, … Write an equation for this arithmetic sequence and find the. You can boost up your problem solving on arithmetic and geometric progressions through this wiki. Geometric sequence can be defined by a series where a fixed amount is multiplied to reach at each of the number of the series, starting from the first. In addition, they can write two equations for the nth terms of geometric sequences and also extend the formula to find a term in a geometric sequence given a term in the sequence and the common ratio. Four real world problems are included in this Geometric Sequences and Series resource. Sequence A : Sequence B : Solution: Sequence A is an arithmetic sequence since every. Let us consider a G. Khan Academy 156,911 views. 5)&Determine&the&number&of&terms&in&each&arithmetic&sequence& a)&38,36,34,…!!,−20& & & & & b)&D5,D8,D11,&…,&D269& 6)&Determine&!&and&!&and&then&write&the. The president and treasurer each contact three members (round 1), each of whom contact three more members (round 2), each of whom contacts three more members (round 3), etc. Let's first compare sequences to relations or functions from the Algebraic Functions section. Determine the general term of the sequence. 666 Chapter 11 Sequences and Series Geometric Sequences and Series USING GEOMETRIC SEQUENCES AND SERIES In a the ratio of any term to the previous term is constant. You can provide visual aids, which can help your students to learn the first step, the second step, and the third step. Solution: We can use the formula a n = a 1 ⋅ r n-1. We need to know n, a 1, and r. We can write a formula for the n th term of a geometric sequence in the form a n = a r n , where r is the common ratio between successive terms. It also explores particular types of sequence known as arithmetic progressions (APs) and geometric progressions (GPs), and the corresponding series. This maze is a self-checking worksheet that allows students to strengthen their skills at finding unknown terms…. When dealing with total amounts, like in the previous example, we need to add the terms in a sequence. They evaluate a given geometric sequence and determine the number of terms in a geometric series. A geometric series is a series of the form S = a+ar +ar2 +ar3 +ar4 + : Here the rst term is a and we obtain each of the other terms by multiplying the term preceding it by the ratio r. LEADING TO applying the properties of geometric sequences and series to functions. Concept 16: Arithmetic & Geometric Sequences Assessment (Level 4 Example Question Level 3 Example Question Level 2 Example Question Write an equation for this geometric sequence and find the 10th term of the sequence. Improve your math knowledge with free questions in "Identify arithmetic and geometric sequences" and thousands of other math skills. Geometric sequence can be defined by a series where a fixed amount is multiplied to reach at each of the number of the series, starting from the first. Even though this series has infinitely many terms, it has a finite sum! To see this, compute and graph the sum of the first n terms for several values of n. Problems involving Geometric Progressions: Problems with Solutions. • geometric sequence (p. If the second differences in a sequence are constant, a cubic function best models the sequence. The general n-th term of the geometric sequence is. c) Find the value of the 13 th term (as a fraction). B" Throughout the video Sal is 1. Find the sum of the geometric series 128 - 64 + 32 - … to 8 terms. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1)=f(n)+f(n-1) for n ≥ 1. This is a geometric sequence with first terma 5 2, and common ratio quence is the common ratio: given by r 5 a n11 a n 5 2n11 2n 52. This diagram represents an infinite series of divisions. pdf: Download File. For example, suppose an ordinary die is thrown repeatedly until the first time a "1" appears. Arithmetic and Geometric Sequences Worksheet Arithmetic Sequence - is a sequence of terms that have a common _____ between them. Math Word Problems Elementary High School Solve Geometry Free #3838. This sequence is not arithmetic, since the difference between terms is not always the same. 3250 by paying Rs. To nd the sum S, multiply the geometric series by r: rS = ar +ar2 +ar3 +ar4 + :. Find Sn for each series described. Displaying all worksheets related to - Infinite Geometric Series. More Practice Problems with Arithmetic Sequence Formula Direction: Read each arithmetic sequence question carefully, then answer with supporting details. Prove or disprove the following statements. When we want to know a total amount, such as money or rows, we want to use a series (which is a sum ). There are methods and formulas we can use to find the value of a geometric series. The measure of a regular polygon's interior angle is four times bigger than the measure of its external angle. In this worksheet, students find the missing term in geometric sequences. 4 Infinite Geometric Series 677 INFINITE GEOMETRIC SERIES IN REAL LIFE Using an Infinite Series as a Model BALL BOUNCE A ball is dropped from a height of 10 feet. 476 #1-5(eoo) Solutions:D5 - Solutions: 6: Handout:Application of Sequences and Series Lesson:D6 - Application of Sequences and Series Lesson Video:D6 - Application of Sequences and Series HW: p. 1) 2, 12 , 72 , 432 518 2) −1, 5, −25 , 125 104 3) −2, 6, −18 , 54 , −162 −122 4) −2, −12 , −72 , −432 , −2592 −3110 Evaluate each geometric series described. Use the formula for the sum of an infinite geometric series. Each time it hits the ground, it bounces to 80% of its previous height. If there are 6 terms, find the value of the first term. Answers are provided on the last page. Let's first compare sequences to relations or functions from the Algebraic Functions section. Write a rule for the nth term of the geometric sequence. Infinite Geometric Series. Solve the following arithmetic sequences and series. More Practice Problems with Arithmetic Sequence Formula Direction: Read each arithmetic sequence question carefully, then answer with supporting details. Some are quite easy to understand: If r = 1 the sequence converges to 1 since every term is 1, and likewise if r = 0 the sequence converges to 0. Some infinite geometric series have a sum. 666 Chapter 11 Sequences and Series Geometric Sequences and Series USING GEOMETRIC SEQUENCES AND SERIES In a the ratio of any term to the previous term is constant. 15) a 1 = 0. Length word problems (metric) Grade 4 Word Problems Worksheets Read and answer each question: 1. ALGEBRA II Worksheet 11. Next, we will look at the formula for a Finite Geometric Series, and how to use it to find the sum of the first n terms of a Geometric sequence. Arithmetic and Geometric Sequences Worksheet Arithmetic Sequence - is a sequence of terms that have a common _____ between them. But 20% is equivalent to 0. 20 in the first month and then increases the payment by Rs. To build the triangle, start with "1" at the top, then continue placing numbers below it in a triangular pattern. The president and treasurer each contact three members (round 1), each of whom contact three more members (round 2), each of whom contacts three more members (round 3), etc. Consider a stock that grows by 10% in year one, declines by 20% in. SOLUTION a. 1 (geometric series). xml CUAU031-EVANS September 4, 2008 13:53 260 Essential Further Mathematics - Module 1 Number patterns and applications Exercise 9A 1 Label each of the sequences as either rule based or probably random. Given the first term and the common ratio of a geometric sequence find the first five terms and the explicit formula. On top of the building, there is a flag pole of 2 m. Activity Based Learning with Task Cards really does work to help reinforce your lessons. It can be helpful for understanding geometric series to understand arithmetic series, and both concepts will be used in upper-level Calculus topics. 1 Sequences We call a list of numbers written down in succession a sequence; for example, the numbers drawn in a lottery:. 1) a n = 40 - 5n 2) a n = 176 - 200n Determine if the sequence is arithmetic. Get Started. 17) a 1 = −4, r = 6 18) a 1. Sample Problem. You can boost up your problem solving on arithmetic and geometric progressions through this wiki. Arithmetic and Geometric Sequences DRAFT. Solution: there are two geometric progressions. Word problems on ages. Make sure you hit all the problems listed in this page. Khan Academy 156,911 views. Practice/Homework:Solve on a separate sheet of paper For each sequence, state if it is arithmetic, geometric, or neither. If rule based, write down the next value in the sequence. Jan 28, 2013 (Monday, Jan 21, 2013 is a holiday) consists of all problems (designated by the word Problem),unless otherwise stated. Arithmetic and Geometric Sequences and Series: Applications For each of the problems below: A. Tuesday April 4: Page 838 - Sigma Notation (College Algebra) Wednesday April 5: Page 851 (College Algebra) Problems: 35-52. You have won contest sponsored by a local radio station. 6) A geometric series has a sum of 1365. Geometric Comparison questions are on the High School Placement Test Order Now Order PDF Download Version - $19. The word "countable" means that you can label. A geometric series is a geometric progression with plus signs between the terms instead of commas. ) is a sequence in which each term except the first is obtained by multiplying the previous term by a non-zero constant called the common ratio. Practice Problems 13 : Ratio and Root tests, Leibniz test 1. With the adoption of the Common Core curriculum, a new topic added to Algebra 2 is sequences. Another simple way of generating a sequence is to start with a number "a" and repeatedly multiply it by a fixed nonzero constant "r". Some workers are paving a dirt road. To find a common ratio in a geometric sequence, multiply any term by the previous term. Decide whether the sequence is arithmetic or geometric. 20 in the first month and then increases the payment by Rs. Lacking resources, I created these Guided Notes to introduce the explicit formulas for Arithmetic and Geometric Sequences. Then graph the first six terms of the sequence. The following geometric sequence calculator will help you determine the nth term and the sum of the first n terms of an geometric sequence. Find the eighth term of a geometric sequence for which 1=−3 and =−2. 4 Infinite Geometric Series 677 INFINITE GEOMETRIC SERIES IN REAL LIFE Using an Infinite Series as a Model BALL BOUNCE A ball is dropped from a height of 10 feet. Find the sum of the n terms of the arithmetic series: 10 2. ©l V2D0z1 L29 BKxurt yaF IS 1okf7tSwQaMroe x MLqL 1C t. Write terms of a geometric sequence. So an example of a geometric series is 1+ 1 10 + 1 100 + 1 1000 + We can take the sum of the rst n terms of a geometric series and this is denoted by Sn: Sn = a(1 rn) 1 r Example 5 : Given the rst two terms of a geometric progression as 2 and 4, what. PROBLEM: How many words did the writer write in a week? SOLUTION: The sequence is 890, 760, 630 …. It provides plenty of examples and Arithmetic Sequences. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Unlike hotdogs and burgers, the word problems usually provide some individual quantities. Number q is called a geometric progression ratio. B" Throughout the video Sal is 1. 1 Sequences We call a list of numbers written down in succession a sequence; for example, the numbers drawn in a lottery:. Even if we admit the greater efficiency of the symbolic approach, many good reasons remain for studying geometric solutions of the quadratic. It also explores particular types of sequence known as arithmetic progressions (APs) and geometric progressions (GPs), and the corresponding series. 15 per month. Each term increases by a factor of 4. This website and its content is subject to our Terms and Conditions. Example 7: Solving Application Problems with Geometric Sequences. Time, speed and distance shortcuts. The aim of this series of lessons is to enable students to: • understand the concept of a geometric series • use and manipulate the appropriate formula • apply their knowledge of geometric series to everyday applications • deal with combinations of geometric sequences and series and derive information from them. n, , , , , ,. The worksheets cover the major skills like determining the nature of the series (convergence or divergence), evaluating the sums of the infinite geometric series, summation notation, finding the first term and common ratio and more. n th n^\text {th}. He usually starts out the semester with only 10 questions on the first exam, but for each subsequent exam he writes one and a half as many questions as were on the previous exam!. Consider, if x 1, x 2 …. Does the series P 1 =1 a n converge or diverge? Prove your claim. Math Busters Word Problems reproducible worksheets are designed to help teachers, parents, and tutors use the books from the Math Busters Word Problems series. Use the formula for an infinite geometric series with –1 < r < 1. The formula for the sum of a geometric series is developed and then used to find the sum of a geometric series, given a series of numbers of summation (sigma) notation. 3250 by paying Rs. Find the value of (a) the common ratio;. The patient is told to walk a distance of 5 km the first week, 8 km the second week, 11 km the third week and so on for a period of 10 weeks. In this geometric series activity, high schoolers find the nth term in a sequence. On the contrary, when there is a common ratio between successive terms, represented by 'r, the sequence is said to be geometric. Write terms of a geometric sequence. Notice that this problem actually involves two infinite geometric series. Sample Problem. Geometric Sequence Word Problems Displaying all worksheets related to - Geometric Sequence Word Problems. Math Busters Word Problems reproducible worksheets are designed to help teachers, parents, and tutors use the books from the Math Busters Word Problems series. Arithmetic and geometricprogressions mcTY-apgp-2009-1 This unit introduces sequences and series, and gives some simple examples of each. You bet $1 for hole 1 with a "double or nothing" stipulation for each subsequent hole. The lesson using real world situations and show how you can apply arithmetic and geometric sequences and series formulas to solve problems. Given the terms a 10 = 3 / 512 and a 15 = 3 / 16384 of a geometric sequence, find the exact value of the term a 30 of the sequence. 28 Questions Show answers. Knowledge of relevant formulae is a prerequisite to evaluate the sum of an arithmetic series and determine the number of terms. This quiz is incomplete! To play this quiz, please finish editing it. Students should have the sequence right before they start the work. Arithmetic and Geometric Sequence Examples Name_____ ©e I2J0y1_5D nKHuOtka[ fSioLfmthwQakr_eZ vLxLICC. How do we find the sum to infinity of a geometric sequence? How can we use arithmetic and geometric sequences to model real-world situations? How do we distinguish graphically between an arithmetic and a geometric sequence? 9. Arithmetic and geometricprogressions mcTY-apgp-2009-1 This unit introduces sequences and series, and gives some simple examples of each. 5) a n = 3 ⋅ 3n − 1 Find a 9 6) a n = −2 ⋅ 4n − 1 Find a 10 7) a n = −3 ⋅ 2n − 1 Find a 12 8) a n = −(−3)n − 1 Find a 11 Given the first term and the common ratio of a geometric sequence find the term named in. Distinguish between situations that can be modeled with linear functions and with. In the case of the geometric series, you just need to specify the first term. How many terms of the arithmetic sequence {,3,5,7,…} will give a sum of 96 í? 8. This is a geometric sequence with first terma 5 2, and common ratio quence is the common ratio: given by r 5 a n11 a n 5 2n11 2n 52. Find the sum of the arithmetic series 17 + 27 + 37 ++ 417. Worksheet on Geometric Series 1. Problems 1. 64 + 48 + 36 + 27 + … c. n th n^\text {th}. The ball will travel approximately 168 inches before it finally comes to rest. Geometric series word problems: swing. ½ - 1 + 2 - 4 + … b. Formulas for calculating the Nth term, the sum of the first N terms, and the sum of an infinite number of terms are derived. ALGEBRA II Worksheet 11. General Term: Geometric Sequence - is a sequence of terms that have a common _____ between them. Consider P 1 n=1 a nwhere a n>0 for all n. 25 thousand dollars will be withdrawn this year, and subsequent withdrawals will rise by 1% each year. Direct link to Miss Nebula's post "Throughout the video Sal is 1. -1-Given the explicit formula for an arithmetic sequence find the first five terms. Some workers are paving a dirt road. Let's first compare sequences to relations or functions from the Algebraic Functions section. Tuesday April 4: Page 838 - Sigma Notation (College Algebra) Wednesday April 5: Page 851 (College Algebra) Problems: 35-52. 2 in place of 20%. The example we just presented describes an increasing geometric sequence. A geometric sequence or progression is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed number, called the common ratio. Quiz & Worksheet - Practice with Arithmetic & Geometric Series. They ask you to compute a related quantity or to combine the quantities. The worksheets cover the major skills like determining the nature of the series (convergence or divergence), evaluating the sums of the infinite geometric series, summation notation, finding the first term and common ratio and more. A geometric series is a series or summation that sums the terms of a geometric sequence. 8 ARITHMETIC AND GEOMETRIC SEQUENCE WORD PROBLEM EXAMPLES All final solutions MUST use the formula. Students should have the sequence right before they start the work. Write a formula for the student population. Finite geometric series word problem: mortgage | Housing | Finance & Capital Markets | Khan Academy - Duration: 17:36. 75 S 3= 1 2 + 1 4 + 1 8 ≈ 0. Tuesday April 4: Page 838 - Sigma Notation (College Algebra) Wednesday April 5: Page 851 (College Algebra) Problems: 35-52. Geometric Series Problem 1 The large outer square has side length 1. Geometric Series Questions Geometric Series - Past Edexcel Exam Questions 1. Title: Skills Practice Geometric Sequences Answer Key Keywords: Skills Practice Geometric Sequences Answer Key Created Date: 9/5/2014 2:46:25 PM Skills Practice Geometric Sequences Answer Key. 28 KB) Add to cart Your students will practice finding the ratio, determining a specific term, and finding the sum of a geometric sequence. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. 1 SEQUENCES SUGGESTED TIME AND EMPHASIS 1 class Essential material After the students have warmed up by doing one or two of the problems as a class, have them start working The analysis and applications of geometric series. Sample Problem. How do we find the sum to infinity of a geometric sequence? How can we use arithmetic and geometric sequences to model real-world situations? How do we distinguish graphically between an arithmetic and a geometric sequence? 9. Another simple way of generating a sequence is to start with a number "a" and repeatedly multiply it by a fixed nonzero constant "r". BASE 10 When the common ratio of a geometric series is 10, the sum is sometimes easier to compute because we use a decimal number system. 5)&Determine&the&number&of&terms&in&each&arithmetic&sequence& a)&38,36,34,…!!,−20& & & & & b)&D5,D8,D11,&…,&D269& 6)&Determine&!&and&!&and&then&write&the. They ask you to compute a related quantity or to combine the quantities. 75 S 3= 1 2 + 1 4 + 1 8 ≈ 0. When the general term is found, then one can find any term in the sequence without writing all the preceding terms. 8 , r = −5 16) a 1 = 1, r = 2 Given the first term and the common ratio of a geometric sequence find the recursive formula and the three terms in the sequence after the last one given. The geometric distribution So far, we have seen only examples of random variables that have a finite number of possible values. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Find the eighth term of a geometric sequence for which 1=−3 and =−2. Write a formula for the student population. Find the sum of the geometric series 128 - 64 + 32 - … to 8 terms. Then find the fifth term in the sequence: a1 = 3,r = −3. 𝑎2=15,𝑟= 1 2 8. You can boost up your problem solving on arithmetic and geometric progressions through this wiki. Click on the "Solution" link for each problem to go to the page containing the solution. Edgar is getting better at math. 20 in the first month and then increases the payment by Rs. The following geometric sequence calculator will help you determine the nth term and the sum of the first n terms of an geometric sequence. Sum of a geometric progression. Let us consider a G. This is the currently selected item. We tried to locate some good of Geometric Sequences and Series Worksheet Answers and Arithmetic Sequence Word Problems Worksheet with Answers Luxury image to suit your needs. d) By considering the infinite geometric series formed by the area of the small triangles, find an expression for the total area, in terms of a , b and c. 64 + 48 + 36 + 27 + … c. An arithmetic series is essentially the sum of the terms contained in an arithmetic sequence. When contestants answer a question wrong their game is over and they get to keep 1 10 of their total winnings up to that point. For those who are visually, as opposed to symbolically, oriented, studying geometric solutions can make both the problems themselves and the algebra involved more. Geometric sequence can be defined by a series where a fixed amount is multiplied to reach at each of the number of the series, starting from the first. a) Prove that your sequence is arithmetic. Geometric Sequences Algebra 1 Name: _____ You go out golfing with a friend and decide to make a friendly wager. Sequences and Series. Displaying all worksheets related to - Geometric Sequence Word Problem. Arithmetic Sequence Practice Problems with Answers 1) Tell whether if the sequence is arithmetic or not. Powered by Create your own unique website with customizable templates. Finite geometric series word problems Our mission is to provide a free, world-class education to anyone, anywhere. Use the formula for the general term of a geometric sequence. )The rst term is a,thenumberris called the ratio (note to get from one term to the next term you multiply by the ratio) and arn is the last term. The situation can be modeled by a geometric sequence with an. 6) A geometric series has a sum of 1365. n such that the. You will receive your score and answers at the end. For example, what is the sum of PDF Pass Chapter 10 24 Glencoe Algebra 2 10-3 Enrichment Half the Distance. The main thing to remember about word problems with sequences and series is that when we want an amount for a single thing, such as a particular row, year, for example, we use a sequence. BASE 10 When the common ratio of a geometric series is 10, the sum is sometimes easier to compute because we use a decimal number system. Math Analysis Honors - Worksheet 51 Geometric Series Given two terms in a geometric sequence find the explicit formula and the recursive formula. Word problems on average speed Word problems on sum of the angles of a triangle is 180 degree. 2-3 W1/15/2020 9. Falling, Rebounding, Use the formula for an infinite geometric series with -1 < r < 1. pdf DOWNLOAD HERE. 5 From Algebra: Themes, Tools, Concepts, by Anita Wah and Henri Picciotto, Teacher's Guide Equations Even though the word is not mentioned, these problems give students another opportunity to think about the mean. Math Word Problems Elementary High School Solve Geometry Free #3838. BASE 10 When the common ratio of a geometric series is 10, the sum is sometimes easier to compute because we use a decimal number system. For example, suppose an ordinary die is thrown repeatedly until the first time a "1" appears. Khan Academy is a 501(c)(3) nonprofit organization. Vold is a sadistic teacher who likes writing lots of exam questions. The general n-th term of the geometric sequence is. Solution: there are two geometric progressions. General Term: Geometric Sequence - is a sequence of terms that have a common _____ between them. (a) If a n+1 an <1 for all nthen the series converges. X n are the observation, then the G. You will need to determine if the series is arithmetic or geometric. Sample Problem. If a square has an area of 49 ft2, what is the length of one of its sides? The perimeter? how long must its length be. b) Prove that your sequence is. Concept 16: Arithmetic & Geometric Sequences Assessment (Level 4 Example Question Level 3 Example Question Level 2 Example Question Write an equation for this geometric sequence and find the 10th term of the sequence. a=5, Find the first 4 terms of the geometric sequence with a=-6 and r= -2/3. Exercises. Bouncing Ball Problem and Geometric Series A Motivating Example for Module 3 Project Description This project demonstrates the following concepts in integral calculus: 1. Does the series P 1 n=1 a n converge or diverge? Prove your claim. HW #15 - Finite Geometric Series 2/17: File Size: 30 kb: File Type: docx: Download File. If the second differences in a sequence are constant, a cubic function best models the sequence. A geometric series is a geometric progression with plus signs between the terms instead of commas. Determine the general term for the sequence. PDF version The Arithmetic Mean-Geometric Mean Inequality (AM-GM Inquality) is a fundamental. Improve your math knowledge with free questions in "Geometric sequences with fractions" and thousands of other math skills. Geometric sequence can be defined by a series where a fixed amount is multiplied to reach at each of the number of the series, starting from the first. B" Throughout the video Sal is 1. 17) a 1 = −4, r = 6 18) a 1. A geometric series has terms that are (possibly a constant times) the successive powers of a number. Unit 6 real life application of Arithmetic and Geometric Sequence. Then graph the first six terms of the sequence. Math Analysis Honors - Worksheet 51 Geometric Series Given two terms in a geometric sequence find the explicit formula and the recursive formula. 666 Chapter 11 Sequences and Series Geometric Sequences and Series USING GEOMETRIC SEQUENCES AND SERIES In a the ratio of any term to the previous term is constant. 19) An auditorium contains 10 seats in the first row, 12 seats in the second, 14 in the third, and so on. 5) a 1 = −9, d = 2 Find a 20 6) a 1 = −14 , d = −10 Find a 38 Given the first term and the common ratio of a geometric sequence find the term named in the problem. that the amounts won for each successive question is a term of a geometric series. Geometry (from the Ancient Greek: γεωμετρία; geo-"earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space Arithmetic and geometric sequence questions and answers. Arithmetic and Geometric Sequences Practice Homework For each Sequence, Pattern, Table, or Story below identify whether it is Arithmetic or Geometric, find the common difference or common ratio, write an Explicit Formula, then use your formulas to find the given term. The value of the stock at the end of each year is therefore described by the geometric sequence 10 ,10. The graph forms a set of discrete points lying on the exponential function This illustrates that a geometric sequence with a positive common ratio other than 1 is an exponential function whose domain is the set of positive integers. Guidelines to use the calculator If you select a n, n is the nth term of the sequence If you select S n, n is the first n term of the sequence Tough Algebra Word Problems. Geometric sequence can be defined by a series where a fixed amount is multiplied to reach at each of the number of the series, starting from the first. word problems finite geometric series Problem 1 : A man repays an amount of Rs. M is defined as:. 17) a 1 = −4, r = 6 18) a 1. (a) If a n+1 an <1 for all nthen the series converges. Show Step-by-step Solutions Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions. So an example of a geometric series is 1+ 1 10 + 1 100 + 1 1000 + We can take the sum of the rst n terms of a geometric series and this is denoted by Sn: Sn = a(1 rn) 1 r Example 5 : Given the rst two terms of a geometric progression as 2 and 4, what. HW #18 - Review. 470 #11, 13-20 p. Decide whether the sequence is arithmetic or geometric. Using the Arithmetic Mean-Geometric Mean Inequality in Problem Solving by JIM WILSON A Presentation to the Annual Meeting of School Mathematics and Science Association, Birmingham, November 8, 2012, was prepared using some parts of this paper. This series is so special because it will enable us to find such things as Power Series and Power Functions in Calculus!. Engaging math & science practice! Improve your skills with free problems in 'Solving Word Problems Using Arithmetic Series' and thousands of other practice lessons. 20 in the first month and then increases the payment by Rs. A geometric sequence is created by repeatedly multiplying an initial number by a constant. For example, suppose an ordinary die is thrown repeatedly until the first time a "1" appears. The bank offers a 4. HW #15 - Finite Geometric Series 2/17: File Size: 30 kb: File Type: docx: Download File. Solve the following arithmetic sequences and series. Using a n 2n, the values a 2 a 1, a 3 a 2, a 4 a 3, a 152 a 352358anda 10 5 2 must all be the same. Geometric sequence can be defined by a series where a fixed amount is multiplied to reach at each of the number of the series, starting from the first. Quiz & Worksheet - Practice with Arithmetic & Geometric Series. Download File PDF Arithmetic Word Problems With Solutions Math Help Fast (from someone who can actually explain it) See the real life story of how a cartoon dude got the better of math Arithmetic Sequences and Geometric Series - Word Problems This. Arithmetic and geometricprogressions mcTY-apgp-2009-1 This unit introduces sequences and series, and gives some simple examples of each. If the second differences in a sequence are constant, a cubic function best models the sequence. De nition 1. Graph the sequence. A tricky geometry word problem Word problem #5: The midpoint of a segment is (3, 6). Does the series P 1 =1 a n converge or diverge? Prove your claim. Arithmetic and Geometric Sequences and Series: Applications For each of the problems below: A. Calculate the area of the first 10 rectangles. Estimate the student population in 2020. Calculus II. Solution: We can use the formula a n = a 1 ⋅ r n-1. 5) Σ k = 1 7 4k − 1 5461 6) Σ i = 1 8. Geometric series word problems: swing. Friday, March 10 Review/Activity KEY Monday, March 13 Review (blank) Review (KEY) Tuesday, March 14 Seq. 3250 by paying Rs. There are methods and formulas we can use to find the value of a geometric series. To get the x-coordinate of the midpoint, you will need to do the math below:. Played 358 times. (b) If a n+1 an >1 for all nthen the series diverges. Find the total distance traveled by the ball. Unit 6 Mod 12. The value of the stock at the end of each year is therefore described by the geometric sequence 10 ,10. We now divide the terms a 10 and a 15 to write. This is the currently selected item. 15) a 1 = 0. 13) a 2 = 12, r = -3 Find a 9 14) a 5 = -64, r = -2 Find a 10 Given two terms in a geometric sequence find the common ratio, the term named in the problem, and the. n Section. Key stage: QUESTION 1 of 10. Math Busters Word Problems reproducible worksheets are designed to help teachers, parents, and tutors use the books from the Math Busters Word Problems series. Sequence And Series Geometric Series Arithmetic Map Activities Word Problems Worksheets Writing Math Words This set of arithmetic sequence worksheets covers the topic like finding the first term, common difference and number of terms; writing general term of an arithmetic sequence, finding the specific term and more!. Show that the series. 2 The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve real-world problems, including writing the first n terms, finding the nth term, and. The worksheets cover the major skills like determining the nature of the series (convergence or divergence), evaluating the sums of the infinite geometric series, summation notation, finding the first term and common ratio and more. Geometric sequence is a list of numbers where each term is obtained by multiplying the previous term by a constant. There are examples, "You-Dos" (student practice problems), and word problems as wel. )The rst term is a,thenumberris called the ratio (note to get from one term to the next term you multiply by the ratio) and arn is the last term. A mathematician who works in the field of geometry is called a geometer. 8 ARITHMETIC AND GEOMETRIC SEQUENCE WORD PROBLEM EXAMPLES All final solutions MUST use the formula. Arithmetic Sequences and Geometric Sequences This algebra 1 and 2 video provides an overview of arithmetic sequence geometric series. 19) Write the following Geometric series in sigma notation: 6 + 12 + 24 + + 384 20) Determine how many seats are in an auditorium with 30 rows of seats if there are 20 seats in the first row, 24 seats in the second row, 28 seats in the third row, and so on. 19) An auditorium contains 10 seats in the first row, 12 seats in the second, 14 in the third, and so on. Tuesday April 4: Page 838 - Sigma Notation (College Algebra) Wednesday April 5: Page 851 (College Algebra) Problems: 35-52. and the three terms in the sequence after the last one given. 1, 2, 4, 8, 16, 32, 64, 128, 256, This sequence has a factor of 2 between each number. Write a rule for the nth term of the geometric sequence. This lesson covers finding the sum of a geometric series using the formula and the calculator. Percentage shortcuts. 5 From Algebra: Themes, Tools, Concepts, by Anita Wah and Henri Picciotto, Teacher's Guide Equations Even though the word is not mentioned, these problems give students another opportunity to think about the mean. Part 2: Geometric Sequences Consider the sequence $2, 4, 8, 16, 32, 64, \ldots$. Say hello to a different functioning and operating style of handling sequence and sums of arithmetic problems and solutions as the installation of the arithmetic sequence and sums will make your mind easy. Is there an example where we don. Word problems included. We can write a formula for the n th term of a geometric sequence in the form a n = a r n , where r is the common ratio between successive terms. Intro to Practice Problems. A sequence of numbers \(\left\{ {{a_n}} \right\}\) is called a geometric sequence if the quotient of successive terms is a constant, called the common ratio. There are examples, "You-Dos" (student practice problems), and word problems as wel. Displaying all worksheets related to - Infinite Geometric Series. Percentage shortcuts. In a Geometric Sequence each term is found by multiplying the previous term by a constant. One series involves the ball falling, while the other series involves the ball rebounding. Word Problems. With the adoption of the Common Core curriculum, a new topic added to Algebra 2 is sequences. com, a math practice program for schools and individual families. 4 (applying the geometric series result) In-class Exercise 11. Find the value of (a) the common ratio;.

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