## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 10 - Section 10.3 - Geoetric Sequences and Series - Exercise Set - Page 1074: 54

#### Answer

The geometric sequence and the common ratio is $r=\dfrac{1}{2}$.

#### Work Step by Step

We are given that $a_n=(\dfrac{1}{2})^n$ Here, we have the first four terms $a_1=\dfrac{1}{2}, a_2=\dfrac{1}{4},a_3=\dfrac{1}{8},a_4=\dfrac{1}{16}$ when $n=1,2,3,4$ Now, subtract each two consecutive terms as below: $a_2/a_1=\dfrac{1/4}{1/2}=\dfrac{1}{2}; a_3/a_2=\dfrac{1}{2}; a_4/a_3=\dfrac{1/16}{1/8}=\dfrac{1}{2}$ We can see that this is the geometric sequence and the common ratio is $r=\dfrac{1}{2}$.

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