College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Section 8.1 - Sequences and Summation Notation - 8.1 Exercises: 33

Answer

$a_{n}=(-1)^{n+1}\ 5^{n}$

Work Step by Step

We are given: $5, -25, 125, -625$, ... We see that the terms in the sequence take on powers of $5$. In addition, we notice that the sign alternates. We find the pattern: $a_1=(-1)^{2}\ 5^{1}$ $a_2=(-1)^{3}\ 5^{2}$ $a_3=(-1)^{4}\ 5^{3}$ $a_4=(-1)^{5}\ 5^{4}$ ... $a_{n}=(-1)^{n+1}\ 5^{n}$
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