Geometric

Adding the terms of the sequence is required to solve many applications of sequences. The sum of the terms of a sequence is called a **series**. A **geometric series** is the sum of the terms of a geometric sequence. For example, the sum of the first five terms of a geometric sequence is represented by:

*S _{5} = a_{1} + a_{2} + a_{3} + a_{4} + a_{5}*

In general, the sum of the first *n* terms of a geometric sequence is:

*S _{n} = a_{1} + a_{2} + a_{3} + a_{4} + ... + a_{n}*

For a geometric sequence with first term a_{1}*, *a common ratio of *r*, and *n* terms the series is given by the formula: