### Topic Page: Arithmetic progression

**arithmetic progression (arithmetic sequence)**

*The Penguin Dictionary of Mathematics*

A sequence in which each term (except the first) differs from the previous one by a constant amount, the common difference. If the first term is a and the common difference is d, then the progression takes the form

a, a + d, a + 2d, a + 3d, …

and the nth term is

a + (n-1)d

A sum of the terms of such a progression is an arithmetic series:

a + (a + d) + (a + 2d) + ….

The sum of the first n terms is given by

na + 1/2n(n - 1)d

or alternatively by

1/2n[2a+(n - 1)d]

Compare geometric progression.

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