Answer
$\displaystyle \frac{93}{16}$
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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$S_{n}=3\displaystyle \cdot\frac{1-(\frac{1}{2})^{5}}{1-\frac{1}{2}}$
$=3\displaystyle \times\frac{\frac{31}{32}}{\frac{1}{2}}=\frac{3\times 31\times 2}{32}$
$=\displaystyle \frac{93}{16}$
$=5.8125$