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**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 .