Answer
$\displaystyle \frac{211}{27}$
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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$S_{n}=3\displaystyle \times\cdot\frac{1-(\frac{2}{3})^{5}}{1-(\frac{2}{3})}=3\times\frac{3^{5}-2^{5}}{3^{5}}\div\frac{1}{3}$
$= 3\displaystyle \times\frac{211}{3^{5}}\times 3$
$=\displaystyle \frac{211}{27}$
