### Topic Page: Arithmetic progression

**arithmetic progression**from

*Greenwood Dictionary of Education*

A list of numbers in which there is one common difference between any and all consecutive numbers in the list. For example, the list {1, 2, 3} is an arithmetic progression because between 2 and 1 the difference is 1, between 3 and 2 the difference is 1, and thus between all consecutive numbers in the list, there is a single common difference. Additionally, the common difference may be negative or less than one. (dbc)

**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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