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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:


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 .

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