## College Algebra (10th Edition)

Published by Pearson

# Chapter 9 - Section 9.3 - Geometric Sequences; Geometric Series - 9.3 Assess Your Understanding: 13

#### Answer

The sequence is geometric with a common ratio of $2$. The first four terms are: $c_1=\frac{1}{4}$ $c_2=\frac{1}{2}$ $c_3=1$ $c_4=2$

#### Work Step by Step

Substitute $1, 2, 3,$ and $4$ for $n$ into the given formula: $c_1=\dfrac{2^{1-1}}{4} = \dfrac{2^0}{4}=\dfrac{1}{4}$ $c_2=\dfrac{2^{2-1}}{4} = \dfrac{2^1}{4}=\dfrac{2}{4}=\dfrac{1}{2}$ $c_3=\dfrac{2^{3-1}}{4} = \dfrac{2^2}{4}=\dfrac{4}{4}=1$ $c_4=\dfrac{2^{4-1}}{4} = \dfrac{2^3}{4}=\dfrac{8}{4}=2$ Notice the the next term is equal to $2$ times the current term. This means that a common ratio of $2$ exists, and the sequence is geometric.

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