(a) Explanation Given: The n th terms of a sequence is, a n = 5 2 ( − 1 2 ) n − 1 (1) Calculation: The first five terms are denoted by, a 1 , a 2 , a 3 , a 4 , a 5 . Substitute n = 1 in the equation (1) and find the first term. a 1 = 5 2 ( − 1 2 ) 1 − 1 = 5 2 ( − 1 2 ) 0 = 5 2 Substitute n = 2 in the equation (1) and find the second term. a 2 = 5 2 ( − 1 2 ) 2 − 1 = 5 2 ( − 1 2 ) 1 = 5 2 ( − 1 2 ) = − 5 4 Substitute n = 3 in the equation (1) and find the third term (b) To determine The common ratio of the geometric sequence if the n th term of the geometric sequence is a n = 5 2 ( − 1 2 ) n − 1 . (c) To determine To graph: The first five terms obtained in part (a).

Precalculus: Mathematics for Calculus (Standalone Book)

7th Edition

ISBN: 9781305071759

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Brooks Cole

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 12.3, Problem 7E

(a)

To determine

The first five terms of the geometric sequence if the nth term of a sequence is an=52(−12)n−1 .

(b)

To determine

The common ratio of the geometric sequence if the nth term of the geometric sequence is an=52(−12)n−1 .

(c)

To determine

To graph: The first five terms obtained in part (a).

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Chapter 12.3, Problem 6E

Chapter 12.3, Problem 8E

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Chapter 12 Solutions

Precalculus: Mathematics for Calculus (Standalone Book)

Ch. 12.1 - A sequence is a function whose domain is...Ch. 12.1 - Prob. 2E Ch. 12.1 - Terms of a Sequence Find the first four terms and...Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Terms of a Sequence Find the first four terms and...Ch. 12.1 - Prob. 7E Ch. 12.1 - Prob. 8E Ch. 12.1 - Terms of a Sequence Find the first four terms and...Ch. 12.1 - Prob. 10E

Ch. 12.1 - Prob. 11E Ch. 12.1 - Prob. 12E Ch. 12.1 - Prob. 13E Ch. 12.1 - Prob. 14E Ch. 12.1 - Recursive Sequences A sequence is defined...Ch. 12.1 - Recursive Sequences A sequence is defined...Ch. 12.1 - Prob. 17E Ch. 12.1 - Prob. 18E Ch. 12.1 - Prob. 19E Ch. 12.1 - Prob. 20E Ch. 12.1 - Prob. 21E Ch. 12.1 - Prob. 22E Ch. 12.1 - Terms of a Sequence Use a graphing calculator to...Ch. 12.1 - Prob. 24E Ch. 12.1 - Prob. 25E Ch. 12.1 - Prob. 26E Ch. 12.1 - Prob. 27E Ch. 12.1 - Prob. 28E Ch. 12.1 - nth term of a Sequence Find the nth term of a...Ch. 12.1 - Prob. 30E Ch. 12.1 - Prob. 31E Ch. 12.1 - Prob. 32E Ch. 12.1 - Prob. 33E Ch. 12.1 - Prob. 34E Ch. 12.1 - Prob. 35E Ch. 12.1 - Prob. 36E Ch. 12.1 - Prob. 37E Ch. 12.1 - Prob. 38E Ch. 12.1 - Prob. 39E Ch. 12.1 - Prob. 40E Ch. 12.1 - Partial Sums Find the first six partial sums S1,...Ch. 12.1 - Prob. 42E Ch. 12.1 - nth Partial Sum Find the first four partial sums...Ch. 12.1 - Prob. 44E Ch. 12.1 - nth Partial Sum Find the first four partial sums...Ch. 12.1 - nth Partial Sum Find the first four partial sums...Ch. 12.1 - Prob. 47E Ch. 12.1 - Prob. 48E Ch. 12.1 - Prob. 49E Ch. 12.1 - Prob. 50E Ch. 12.1 - Prob. 51E Ch. 12.1 - Prob. 52E Ch. 12.1 - Prob. 53E Ch. 12.1 - Prob. 54E Ch. 12.1 - Prob. 55E Ch. 12.1 - Evaluating a Sum Use a graphing calculator to...Ch. 12.1 - Prob. 57E Ch. 12.1 - Prob. 58E Ch. 12.1 - Prob. 59E Ch. 12.1 - Prob. 60E Ch. 12.1 - Prob. 61E Ch. 12.1 - Prob. 62E Ch. 12.1 - Prob. 63E Ch. 12.1 - Prob. 64E Ch. 12.1 - Prob. 65E Ch. 12.1 - Sigma Notation Write the sum without using sigma...Ch. 12.1 - Sigma Notation Write the sum using sigma notation....Ch. 12.1 - Prob. 68E Ch. 12.1 - Prob. 69E Ch. 12.1 - Sigma Notation Write the sum using sigma notation....Ch. 12.1 - Sigma Notation Write the sum using sigma notation....Ch. 12.1 - Prob. 72E Ch. 12.1 - Prob. 73E Ch. 12.1 - Prob. 74E Ch. 12.1 - nth Term of a Sequence Find a formula for the nth...Ch. 12.1 - Compound Interest Julio deposits 2000 in a savings...Ch. 12.1 - Prob. 78E Ch. 12.1 - Population of a City A city was incorporated in...Ch. 12.1 - Paying off a Debt Margarita borrows 10,000 from...Ch. 12.1 - Fish Farming A fish farmer has 5000 catfish in his...Ch. 12.1 - Prob. 82E Ch. 12.1 - Prob. 83E Ch. 12.1 - Concentration of a Solution A biologist is trying...Ch. 12.1 - Prob. 85E Ch. 12.1 - DISCOVER PROVE: Different Sequences That Start the...Ch. 12.1 - Prob. 87E Ch. 12.1 - Prob. 88E Ch. 12.2 - An arithmetic sequence is a sequence in which the...Ch. 12.2 - Prob. 2E Ch. 12.2 - Prob. 3E Ch. 12.2 - Prob. 4E Ch. 12.2 - Prob. 5E Ch. 12.2 - Prob. 6E Ch. 12.2 - Prob. 7E Ch. 12.2 - Prob. 8E Ch. 12.2 - Prob. 9E Ch. 12.2 - Prob. 10E Ch. 12.2 - Prob. 11E Ch. 12.2 - Prob. 12E Ch. 12.2 - Prob. 13E Ch. 12.2 - Prob. 14E Ch. 12.2 - Prob. 15E Ch. 12.2 - Prob. 16E Ch. 12.2 - Prob. 17E Ch. 12.2 - Prob. 18E Ch. 12.2 - Prob. 19E Ch. 12.2 - Prob. 20E Ch. 12.2 - Prob. 21E Ch. 12.2 - Prob. 22E Ch. 12.2 - Prob. 23E Ch. 12.2 - Prob. 24E Ch. 12.2 - Prob. 25E Ch. 12.2 - Prob. 26E Ch. 12.2 - Prob. 27E Ch. 12.2 - Arithmetic Sequence? 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The first five terms of the geometric sequence if the n th term of a sequence is a n = 5 2 ( − 1 2 ) n − 1 .

Solution Summary: The author calculates the first five terms of the geometric sequence if the nth term of a sequence is a_n=52

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The first five terms of the geometric sequence if the nth term of a sequence is an=52(−12)n−1 .

The common ratio of the geometric sequence if the nth term of the geometric sequence is an=52(−12)n−1 .

To graph: The first five terms obtained in part (a).

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Chapter 12 Solutions