Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 11 - Further Topics in Algebra - 11.3 Geometric Sequences and Series - 11.3 Exercises: 24

Answer

$a_{5}=a_{1}\times r^{4}=\dfrac {1}{2}\times \left( \dfrac {4}{3}\right) ^{4}=\dfrac {128}{81};$ $a_{n}=a_{1}\times r^{n-1}=\dfrac {1}{2}\times \left( \dfrac {4}{3}\right) ^{n-1}$

Work Step by Step

$r=\dfrac {\dfrac {32}{27}}{\dfrac {8}{9}}=\dfrac {\dfrac {8}{9}}{\dfrac {2}{3}}=\dfrac {\dfrac {2}{3}}{\dfrac {1}{2}}=\dfrac {9}{3};a_{1}=\dfrac {1}{2}\Rightarrow a_{5}=a_{1}\times r^{4}=\dfrac {1}{2}\times \left( \dfrac {4}{3}\right) ^{4}=\dfrac {128}{81};a_{n}=a_{1}\times r^{n-1}=\dfrac {1}{2}\times \left( \dfrac {4}{3}\right) ^{n-1}$
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