Arithmetic progression

In mathematics, an arithmetic progression is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. For instance, the sequence 3, 5, 7, 9, 11, ... is an arithmetic progression with common difference 2.

If the initial term of an arithmetic progression is a and the common difference of successive members is d, then the n-th term of the sequence is given by

• a + nd,    n = 0, 1, 2, ... if the initial term is taken as the 0th
• a + (n-1)d,    n = 1, 2, ... if the initial term is taken as the 1st

The first option gives an easier formula, but uses a somewhat confusing terminology.

The sum of the numbers in an arithmetic progression is called an arithmetic series. A convenient formula for arithmetic series is available.

See also geometric progression.