College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 9 - Section 9.1 - Sequences - 9.1 Assess Your Understanding: 34

Answer

$a_n=(-1)^{n+1}(2n)$

Work Step by Step

The terms, when the signs are ignored, are the multiples of $2$. This means that the formula for the $n^{th}$ term involves $2n$. The sign of the terms alternate, starting with positive. This means that the formula for the $n^{th}$ term involves a power of $-1$. Since the first term is positive, the exponent/power of $-1$ is either $n+1$ or $n-1$. If $n+1$ is used, the formula for the $n^{th}$ term is: $a_n=(-1)^{n+1}(2n)$ To check: n=1: $(-1)^{1+1}(2\cdot1) = (-1)^2(2) = 2$ n=2: $(-1)^{2+1}(2\cdot2) = (-1)^3(4) = -4$ n=3: $(-1)^{3+1}(2\cdot3) = (-1)^4(6) = 6$
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