Definition:Arithmetic Sequence

Definition
An arithmetic progression is a sequence $\left \langle{a_n}\right \rangle$ in $\R$ defined as:
 * $a_n = a_1 + \left({n-1}\right) d$ for $n = 1, 2, 3, \ldots$

where:
 * $a_1 \in \R$ is called the initial term
 * $d \in \R: d \ne 0$ is called the common difference.

Thus its general form is:
 * $a_1, a_1 + d, a_1 + 2 d, a_1 + 3 d, \ldots$