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: 42

Answer

$422$

Work Step by Step

$\sum ^{5}_{j=1}243\left( \dfrac {2}{3}\right) ^{j}=\dfrac {a_{1}\left( r^{n}-1\right) }{r-1};a_{1}=243\times \left( \dfrac {2}{3}\right) ^{1}=162;r=\dfrac {2}{3}\Rightarrow S_{n}=\dfrac {162\times \left( \left( \dfrac {2}{3}\right) ^{5}-1\right) }{\dfrac {2}{3}-1}=\dfrac {162\times \left( \dfrac {-211}{243}\right) }{-\dfrac {1}{3}}=422$
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