A geometric series is the sum of the terms in a geometric sequence. $$\begin{array}{rl}\text{Sequence:}& 1,2,4,8\\ \text{Series:}& s=1+2+4+8=15\end{array}$$ Each term in a geometric sequence can be written using the following rule. $$a_n=a_1\cdot r^{n-1}$$ Here, $a_1$ is the first term of the sequence and $r$ is its common ratio. Using these symbols, a formula for the geometric series of a sequence with $n$ terms can be derived.