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# 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 . 