Answer
$\frac{-63}{2}$
Work Step by Step
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
$S_5=\frac{3}{2}(\frac{(-2)^{6}-1}{-2-1})$
$=\frac{-63}{2}$
