## Precalculus (6th Edition) Blitzer

$130.264\text{ inches}$.
From the given information, we can observe that it is a geometric series: $20,0.9\left( 20 \right),{{0.9}^{2}}\left( 20 \right),{{0.9}^{3}}\left( 20 \right)\cdots$ Here ${{a}_{1}}=20$ and common ratio $r=0\cdot 9$ 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{20\left( 1-0\cdot {{9}^{10}} \right)}{\left( 1-0\cdot 9 \right)} \\ & \frac{20\left( 1-0\cdot 3486 \right)}{\left( 0\cdot 1 \right)} \\ & =130.264 \end{align}