## Arithmetic Sequences

An arithmetic sequence (or arithmetic progression, AP) is an ordered set of numbers in which the difference between consecutive values is constant. For example:

2, 6, 10, 14, 18, 22, …

The sum of a sequence is called a series. For example:

2 + 6 + 10 + 14 + 18 + 22 + …

The general term in an arithmetic sequence is given by

The sum of the first terms of an arithmetic sequence is given by

where

- a = first term
- a
_{k} = k^{th} term
- d = common difference
- k = term number
- n = number of terms
- S
_{n} = sum of first n terms of sequence