Answer
$\displaystyle \sum_{n=1}^{8}5(-\frac{5}{2})^{n-1}=-\frac{278835}{128}$
Work Step by Step
$\displaystyle \sum_{n=1}^{8}5(-\frac{5}{2})^{n-1}=5(-\frac{5}{2})^0+5(-\frac{5}{2})^1+...+5(-\frac{5}{2})^7$
$a_1=5(-\frac{5}{2})^0=5$
$r=\frac{a_2}{a_1}=\frac{5(-\frac{5}{2})^1}{5(-\frac{5}{2})^0}=-\frac{5}{2}$
$S_{6}=a_1(\frac{1-r^n}{1-r})=5(\frac{1-(-\frac{5}{2})^{8}}{1-(-\frac{5}{2})})=5·\frac{1-\frac{390625}{256}}{\frac{7}{2}}=
5·\frac{-\frac{390369}{256}}{\frac{7}{2}}=-\frac{278835}{128}$
