Answer
$S_{15}\approx-6.01295424\times10^{9}$
Work Step by Step
$\dfrac{a_{n+1}}{a_n}=\dfrac{7(-4)^{n+1}}{7(-4)^n}=-4$
Since the ratio between consecutive terms is constant, the given sequence is geometric.
The first term is $a_{1}=7(-4)^{1}=-28$
The common ratio $r=-4$.
The formula for the sum of the first $n$ terms is:
$S_{n}=\frac{a_{1}(1-r^{n})}{1-r}$
$S_{15}=\frac{-28(1-(-4)^{15})}{1-(-4)}\approx-6.01295424\times10^{9}$
