Answer
$S_5=\frac{55}{2}$
Work Step by Step
We need to find:
$\sum_{k=1}^{5}8(-\frac{3}{2})^{k-1}$
We see that this is a geometric sequence with $a=8$ and $r=\frac{-3}{2}$.
We know the partial sum of a geometric sequence is:
$S_n=a_1\frac{1-r^n}{1-r}$
$S_5=8\frac{1-(-\frac{3}{2})^{5}}{1-(-\frac{3}{2})}=\frac{55}{2}$
