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 - Page 1034: 26


$a_{5}=a_{1}\times r^{4}=3\times \left( -\dfrac {3}{4}\right) ^{4}=\dfrac {-243}{256};$ $a_{n}=a_{1}\times r^{n-1}=3\times \left( \dfrac {-3}{4}\right) ^{n-1}$

Work Step by Step

$r=\dfrac {\dfrac {-81}{64}}{\dfrac {27}{16}}=\dfrac {\dfrac {27}{16}}{\dfrac {-9}{4}}=\dfrac {\dfrac {-9}{4}}{3}=-\dfrac {3}{4};a_{1}=3\Rightarrow a_{5}=a_{1}\times r^{4}=3\times \left( -\dfrac {3}{4}\right) ^{4}=\dfrac {-243}{256};a_{n}=a_{1}\times r^{n-1}=3\times \left( \dfrac {-3}{4}\right) ^{n-1}$
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