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: 76


$134.066\text{ inches}$.

Work Step by Step

From the given information, we can observe that it is a geometric series $16,0.96\left( 16 \right),{{0.96}^{2}}\left( 16 \right),{{0.96}^{3}}\left( 16 \right),\cdots $ Here ${{a}_{1}}=16$ and common ratio $r=0\cdot 96$ and $n=10$. 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 $\begin{align} & {{S}_{n}}=\frac{16\left( 1-0\cdot {{96}^{10}} \right)}{\left( 1-0\cdot 96 \right)} \\ & =\frac{16\left( 1-0\cdot 6648 \right)}{\left( 0\cdot 04 \right)} \\ & =134.066 \end{align}$
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