[tex] \bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=2\\
r=8\\
n=4
\end{cases}
\\\\\\
S_4=2\left( \cfrac{1-8^4}{1-8} \right)\implies S_4=2\left( \cfrac{-4095}{-7} \right)
\\\\\\
S_4=2(585)\implies S_4=1170 [/tex]
