## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 10 - Section 10.3 - Geoetric Sequences and Series - Concept and Vocabulary Check - Page 1073: 9

#### Answer

$1,-3,9,-27,81,...$ Geometric.

#### Work Step by Step

When we observe the sequence carefully, we see that the difference between two consecutive terms is not the same. Thus, the common ratio will be computed as $1,-3,9,-27,81,...$ Now, ${{a}_{1}}=1,{{a}_{2}}=-3,{{a}_{3}}=9,{{a}_{4}}=-27,{{a}_{5}}=81,...$ So, \begin{align} & \frac{{{a}_{2}}}{{{a}_{1}}}=\frac{\left( -3 \right)}{1} \\ & =-3 \\ & \frac{{{a}_{3}}}{{{a}_{2}}}=\frac{9}{\left( -3 \right)} \\ & =-3 \end{align} \begin{align} & \frac{{{a}_{4}}}{{{a}_{3}}}=\frac{\left( -27 \right)}{9} \\ & =-3 \\ & \frac{{{a}_{5}}}{{{a}_{4}}}=\frac{81}{\left( -27 \right)} \\ & =-3 \end{align} Therefore, the common ratio is -3. Hence, the sequence is Geometric.

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