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: 13


See below.

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. $c_1=\dfrac{2^{(1-1)}}{4}=\dfrac{1}{4}$ $c_2=\dfrac{2^{(2-1)}}{4}=\dfrac{1}{2}$ $c_3=\dfrac{2^{(3-1)}}{4}=\dfrac{2^2}{4}=1$ $c_3=\dfrac{2^{(4-1)}}{4}=\dfrac{2^3}{4}=2$ We see that the the next term is equal to $2$ times the current term and this implies that the sequence is geometric with a common ratio of $2$
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