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 1076: 85


$\$9$ million

Work Step by Step

From the given information, we can observe that it forms a geometric infinite series: $6,\left( 0.6 \right)6,{{\left( 0.6 \right)}^{2}}6,\cdots $ Here ${{a}_{1}}=6$ and common ratio $r=0.6$. We use the formula for the sum of a geometric series: ${{S}_{n}}=\frac{{{a}_{1}}}{\left( 1-r \right)}$. Thus $\begin{align} & {{S}_{n}}=\frac{6}{\left( 1-0.6 \right)} \\ & =\frac{6}{\left( 0.4 \right)} \\ & =15 \end{align}$ So, the spending is $\$15-\$6=\$9$
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