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: 14


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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. $d_1=\dfrac{3^{1}}{9}=\dfrac{1}{3}$ $d_2=\dfrac{3^{2}}{9}=1$ $d_3=\dfrac{3^3}{9}=\dfrac{27}{9}=3$ $d_4=\dfrac{3^{4}}{4}=\dfrac{81}{9}=9$ We see that the the next term is equal to $3$ times the current term and this implies that the sequence is geometric with a common ratio of $3$.
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