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