## Calculus with Applications (10th Edition)

$\frac{-63}{2}$
We are given $\Sigma\frac{3}{2}(-2)^{i}$ with $a=\frac{3}{2}, r=-2$ the summation is from $i=0$ to $n-1=5 \rightarrow n=6$ using the formula $S_{n}=\frac{a(r^{n}-1)}{r-1}$ $r \ne 1$ gives $S_5=\frac{3}{2}(\frac{(-2)^{6}-1}{-2-1})$ $=\frac{-63}{2}$