Answer
$\displaystyle \frac{3^{n}-1}{6}$
Work Step by Step
$a_{2}/a_{1}=3$
$a_{3}/a_{2}=3$
$...$ common ratio.
The terms of the sum form a geometric sequence, $a_{1}=\displaystyle \frac{1}{3},\ r=3.$
THEOREM: Sum of the First $n$ Terms of a Geometric Sequence
$S_{n}=a_{1}\displaystyle \cdot\frac{1-r^{n}}{1-r},\quad r\neq 0,1$
$=\displaystyle \frac{1}{3}\left(\frac{1-3^{n}}{1-3}\right)$
$=\displaystyle \frac{1}{3}\left(\frac{1-3^{n}}{-2}\right)$
$=-\displaystyle \frac{1-3^{n}}{6} $
$=\displaystyle \frac{3^{n}-1}{6}$
