Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 14 - Sequences, Series, and the Binomial Theorem - Mid-Chapter Review - Guided Solutions - Page 915: 2

Answer

$a_7=81$

Work Step by Step

We have to find $7$th term of the geometric sequence: $\frac{1}{9}, -\frac{1}{3}, 1, 3, . . . $ $$a_n=a_1r^{n-1}$$ $$n=7, \quad a_1=\dfrac{1}{9}, \quad r=\frac{-\frac{1}{3}}{\frac{1}{9}}=-3$$ $$a_7=\dfrac{1}{9}(-3)^{7-1}$$ $$a_7=\dfrac{(-3)^6}{9}=\dfrac{(-3)^6}{3^2}=\dfrac{(-1)^63^6}{3^2}$$ $$a_7=3^4=81$$
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