Answer
$27.5$
Work Step by Step
See p. 861.
For the geometric sequence $a_{n}=ar^{n-1}$
the nth partial sum$ S_{n}=\displaystyle \sum_{k=1}^{n}ar^{k-1}$ (where $r\neq 1$)
is given by$ \displaystyle \quad S_{n}=a\cdot\frac{1-r^{n}}{1-r}$
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$S_{n}=8\displaystyle \cdot\frac{1-(-\frac{3}{2})^{5}}{1-(-\frac{3}{2})}=8\times\frac{\frac{32+243}{32}}{\frac{5}{2}}$
$=8\displaystyle \times\frac{\frac{275}{32}}{\frac{5}{2}}=\frac{8\times 275\times 2}{32\times 5}=\frac{55}{2}$
$=27.5$
