Answer
$274,512$
Work Step by Step
$\dfrac{a_{n+1}}{a_n}=\dfrac{2(7^{n+1})}{2(7^n)}=7$
Since the ratio between consecutive terms is constant, the given sequence is geometric.
The first term is $a_1=2(7^1)=14$.
The common ratio is $r=7$.
The formula for the sum of the first $n$ terms is:
$S_{n}=\frac{a_{1}(1-r^{n})}{1-r}$
$S_{6}=\frac{14(1-7^{6})}{1-7}=274,512$
