Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 10 - Section 10.3 - Geoetric Sequences and Series - Exercise Set - Page 1075: 73

Answer

$\$793583$.

Work Step by Step

From the given statement, the series is $24000,1\cdot 05\left( 24000 \right),1\cdot {{05}^{2}}\left( 24000 \right),...$ From the given information, we can observe that it is a geometric series $24000,1\cdot 05\left( 24000 \right),1\cdot {{05}^{2}}\left( 24000 \right),\cdots $ Here ${{a}_{1}}=24000$ and common ratio $r=1\cdot 05$ and $n=20$. We use the formula for the sum of a geometric series with finite terms ${{S}_{n}}=\frac{{{a}_{1}}\left( 1-{{r}^{n}} \right)}{\left( 1-r \right)}$. Thus $\begin{align} & {{S}_{n}}=\frac{24000\left( 1-1\cdot {{05}^{20}} \right)}{\left( 1-1\cdot 05 \right)} \\ & =\frac{24000\left( 1-2\cdot 653 \right)}{-\left( 0\cdot 05 \right)} \\ & =\frac{24000\left( -1\cdot 653 \right)}{-\left( 0\cdot 05 \right)} \\ & =793583 \end{align}$
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