[tex]\bf \sum\limits_{i=a_1}^{a_n}\ a1\cdot (r)^{n-1}\iff S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\qquad
\begin{cases}
a_1=\textit{first term}\\
r=\textit{common ratio}\\
n=n^{th}\ term
\end{cases}\\\\
-----------------------------\\\\
\begin{array}{llll}
\sum\limits_{i=1}^{3}\ &4\cdot \left( \frac{1}{2} \right)^{i-1}\\
&\uparrow \quad \uparrow \\
&a_1\quad r
\end{array}\iff S_3=4\left( \cfrac{1-\left( \frac{1}{2} \right)^3}{1-\left( \frac{1}{2} \right)} \right)[/tex]
