# Chapter 11 - 11.3 - Geometric Sequences and Series - 11.3 Exercises - Page 795: 11

It is a geometric sequence. $r=-\sqrt 7$

#### Work Step by Step

A sequence is geometric if $\frac{a_2}{a_1}=\frac{a_3}{a_2}=\frac{a_4}{a_3}=...=r$ For the given sequence we have that: $\frac{a_2}{a_1}=\frac{-\sqrt 7}{1}=-\sqrt 7$ $\frac{a_3}{a_2}=\frac{7}{-\sqrt 7}=\frac{7}{-\sqrt 7}\frac{\sqrt 7}{\sqrt 7}=\frac{7\sqrt 7}{-(\sqrt 7)^2}=\frac{7\sqrt 7}{-7}=-\sqrt 7$ $\frac{a_4}{a_3}=\frac{-7\sqrt 7}{7}=-\sqrt 7$ It is a geometric sequence. Common ratio: $r=-\sqrt 7$

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