Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 11 - 11.3 - Geometric Sequences and Series - 11.3 Exercises - Page 795: 12


It is a geometric sequence. $r=\frac{2}{\sqrt 3}$

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: $\frac{a_2}{a_1}=\frac{\frac{4}{\sqrt 3}}{2}=\frac{2}{\sqrt 3}$ $\frac{a_3}{a_2}=\frac{\frac{8}{3}}{\frac{4}{\sqrt 3}}=\frac{8}{3}.\frac{\sqrt 3}{4}=\frac{2(4)(\sqrt 3)}{\sqrt 3(\sqrt 3)(4)}=\frac{2}{\sqrt 3}$ $\frac{a_4}{a_3}=\frac{\frac{16}{3\sqrt 3}}{\frac{8}{3}}=\frac{16}{3\sqrt 3}\frac{3}{8}=\frac{2(8)(3)}{3(\sqrt 3)(8)}=\frac{2}{\sqrt 3}$ It is a geometric sequence. Common ratio: $r=\frac{2}{\sqrt 3}$
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