Answer
$\dfrac{364}{2187}$
Work Step by Step
Formula to calculate the sum of the first $n$ terms of a geometric sequence is: $s_n=\dfrac{a(1-r^n)}{(1-r)}$
Here, $r=\dfrac{a_2}{a_1}=\dfrac{1}{3}$
As we are given that, $n=6$
Thus, $s_{6}=\dfrac{\dfrac{1}{9}(1-(\dfrac{1}{3})^{6})}{(1-\dfrac{1}{3})}$
or, $s_{6}=\dfrac{364}{2187}$