Math

Arithmetic Series

An arithmetic series is the sum of an arithmetic sequence in which the difference between consecutive terms is a constant. An arithmetic series has the form:

or

where the general term of the series is given by:

.

The sum of the first n terms of an arithmetic series can be found by using:

.

Another formula for the sum of the first n terms of an arithmetic series can be derived using the formula for the general term of an arithmetic series:

Example: Find the sum of the first six terms of the following arithmetic series: 

For this arithmetic sequence the common difference can be found as:

given that the first term of the series is , we find:

Example: For an arithmetic series  with,find .