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: 24

Answer

a) $-6$ and $7$ b) $a_{n+1} = |a_n + 1| * (-1)^n$, $a_1 = 1$ c) $a_n = (-1)^{n+1} n$

Work Step by Step

a) The absolute value of the number is increasing, with the terms alternating in signs. Thus, the next two terms would be $-6$ and $7$ b) Since the first term is 1, $a_1 = 1$. The absolute value increases by one every iteration and it alternates signs, starting with positive. $a_{n+1} = |a_n + 1| * (-1)^n$ c) The $n$ reflects the absolute value, and the sign is even whenever the $n$ is odd. Thus, the formula would be: $a_n = (-1)^{n+1} n$
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