Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.3 Geometric Sequences; Geometric Series - 11.3 Assess Your Understanding - Page 844: 17


The sequence is geometric with a common ratio of $\dfrac{3}{2}$.

Work Step by Step

We need to substitute $1, 2, 3,$ and $4$ for $n$ into the given equation to find the first four terms. $t_1=\dfrac{3^{1-1}}{2^1}=\dfrac{1}{2} $ $t_2=\dfrac{3^{2-1}}{2^2}=\dfrac{3}{4} $ $t_3=\dfrac{3^{3-1}}{2^3}=\dfrac{9}{8} $ $t_4=\dfrac{3^{4-1}}{2^4}=\dfrac{27}{16} $ We can see that the common ratios are the same; thus the sequence is geometric with a common ratio of $\dfrac{3}{2}$.
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