Definition:Arithmetic Sequence

Definition
An arithmetic sequence is a finite sequence $\sequence {a_k}$ in $\R$ or $\C$ defined as:
 * $a_k = a_0 + k d$ for $k = 0, 1, 2, \ldots, n - 1$

Thus its general form is:
 * $a_0, a_0 + d, a_0 + 2 d, a_0 + 3 d, \ldots, a_0 + \paren {n - 1} d$

Also known as
The term arithmetic progression is usual.

Arithmetical progression is also sometimes seen.

Hence the abbreviation A.P. is well-understood.

However, use of the term progression, although ubiquitous in the literature, is deprecated on on account of the fact that the term is used both for arithmetic sequence and arithmetic series, and this can be a source of confusion.

Also see

 * Sum of Arithmetic Sequence
 * Definition:Arithmetic Series