Geometric Sequence
a_{n+1} = q \cdot a_n
Finite Series
\begin{align*} S_n &= a_1 + a_2 + \cdots + a_{n-1} + a_n \\ q*S_n &= a_2 + a_3 + \cdots + a_n + a_{n+1} \\ S_n - q*S_n &= a_1 - a_{n+1}\\ (1-q)S_n &= a_1 - a_{n+1}\\ S_n &= \frac{a_1-a_{n+1}}{1-q}\\\end{align*}