Sum of the First n Terms of a Geometric Series

If a series is geometric there are ways to find the sum of the first $n$ terms, denoted $S_n$ , without actually adding all of the terms.

To find the sum of the first $n$ terms of a geometric series use the formula
$S_n=\frac{a_1(1-r^n)}{1-r},r\ne 1$ ,
where $n$ is the number of terms, $a_1$ is the first term and $r$ is the common ratio .