Answer
$S_{8} = 85 $
Work Step by Step
Given geometric sequence
$-1,2,-4,...$
$a_{1} = -1$
Common ratio $r = \frac{a_{n}}{a_{n-1}}$
$r= \frac{a_{2}}{a_{1}} = \frac{2}{-1} = -2$
Sum of first eight terms is
$S_{8} = \frac{-1(1-(-2)^{8})}{1-(-2)}$ [Using $S_{n} =\frac{ a_{1}(1-r^{n})}{1-r}$]
$S_{8} = \frac{-1(1-256)}{1+2} $
$S_{8} = \frac{-1(-255)}{3} $
$S_{8} = \frac{255}{3} $
$S_{8} = 85 $