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 - 14.3 Geometric Sequences and Series - 14.3 Exercise Set: 33

Answer

$a_n=\frac{1}{x}\times\frac{1}{x}^{n-1}=(\frac{1}{x})^{n}$

Work Step by Step

The general term in a geometric sequence is: $a_n=a_1\times r^{n-1}$ Here, $a_1=\frac{1}{x}$ We can find the common ratio by dividing two subsequent terms: $r=\frac{a_2}{a_1}=\frac{\frac{1}{x^2}}{\frac{1}{x}}=\frac{x}{x^2}=\frac{1}{x}$ The general term is: $a_n=\frac{1}{x}\times\frac{1}{x}^{n-1}=\frac{1}{x}^{n}$
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