If a series is arithmetic the sum of the first *n* terms, denoted *S _{n}*, there are ways to find its sum without actually adding all of the terms.

To find the sum of the first *n* terms of an arithmetic series use the formula,

,

where *n* is the number of terms, *a*_{1} is the first term and *a _{n}* is the last term.

**Example 1:**

Find the sum of the first 20 terms of the arithmetic series if *a*_{1} = 5 and *a*_{20} = 62.

**Example 2:**

Find the sum of the first 40 terms of the arithmetic series 2 + 5 + 8 + 11 + ···.

First find the 40^{th} term:

Then find the sum:

**Example 3:**

Find the sum:

First find *a*_{1} and *a*_{50}:

* a*_{1} = 3(1) + 2 = 5

*a*_{50} = 3(50) + 2 = 152

Then find the sum: