Answer
$−70.46875$
Work Step by Step
We are given the geometric sum:
$\sum_{k=1}^5 (-2.5)^k$
Rewrite the sum:
$n=5$
$S_5=a+ar+...+ar^4=\sum_{k=0}^4 ar^k=a\dfrac{1-r^5}{1-r}$
The geometric sequence has the ratio $r=-2.5$ and the first term $a=-2.5$.
$S_5=\sum_{k=0}^4 (-2.5)(-2.5)^k=(-2.5)\dfrac{1-(-2.5)^5}{1-(-2.5)}=−70.46875$
