Explanation The given sequence is { a n } = { 3 − n 2 n − 1 } . Recall the definition of geometric sequence, “If the ratio of any consecutive terms in a sequence is constant”. In order to check the ratio of any two consecutive terms in a sequence is constant, it is enough to show that a n a n − 1 is constant. Note that a n and a n − 1 are any two consecutive terms. Substitute n − 1 for n in a n = 3 − n 2 n − 1 to get the value of a n − 1 as follows. a n − 1 = 3 − ( n − 1 ) 2 ( n − 1 ) − 1 = 3 − n + 1 2 ( n − 1 ) − 1 Compute the value of a n a n − 1 . a n a n − 1 = 3 − n 2 n − 1 3 − n + 1 2 ( n − 1 ) − 1 = 3 − n 2

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ISBN: 9780134556079

Author: Sullivan, Michael, III, Struve, Katherine R., Mazzarella, Janet.

Publisher: Pearson,

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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 13.3, Problem 26E

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To show: The sequence {an}={3−n2n−1} is a geometric sequence and find the first term and the common ratio of the sequence.

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Chapter 13.3, Problem 25E

Chapter 13.3, Problem 27E

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Chapter 13 Solutions

Elementary & Intermediate Algebra

Ch. 13.1 - A(n) _____ is a function whose domain is the set...Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

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The sequence { a n } = { 3 − n 2 n − 1 } is a geometric sequence and find the first term and the common ratio of the sequence.

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Chapter 13 Solutions