Skip to main content Skip to Search Box
Summary Article: arithmetic progression (arithmetic sequence)
from 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.

Copyright © Penguin Books Ltd, 1989, 1998, 2003, 2008

Related Articles

Full text Article arithmetic progression
Dictionary of Economics, Wiley

A sequence of numbers, called terms , such that any two consecutive numbers in the sequence are separated by a fixed common difference....

Full text Article arithmetic progression
Academic Press Dictionary of Science and Technology

A sequence in which the difference between any term and its predecessor is some constant. In particular, if a is the first term, then the ...

Full text Article arithmetic progression
Philip's Encyclopedia

Sequence of numbers in which each term is produced by adding a constant term (the common difference d ) to the preceding one. It has the form ...

See more from Credo