Definition:Arithmetic Progression
From ProofWiki
Definition
An arithmetic progression (or arithmetical 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:
- $a_1, a_1 + d, a_1 + 2 d, a_1 + 3 d, \ldots$
