Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 8 - Sequences and Infinite Series - 8.1 An Overview - 8.1 Exercises: 25

Answer

a) $-5$ and $5$ b) $a_{n+1} = -a_n$, $a_1 = -5$ c) $a_n = 5(-1)^{n}$

Work Step by Step

a) The absolute value remains the same while only the signs change. Thus, the next two values are $-5$ and $5$ b) Since the first term is $-5$, $a_1 = -5$ The recursion should only affect the sign of the term. $a_{n+1} = -a_n$ c) The only thing that changes as the sequence continues is the sign of the number $5$. Every time $n$ is an odd number, the term is $-5$. $a_n = 5(-1)^{n}$
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