Arithmetic Progressions

A sequence in which every term

A sequence in which every term after the first is found by adding a fixed number to the previous term. The general form is a, a + d, a + 2d, a + 3d, .

To know an AP completely

To know an AP completely, both the first term a and the common difference d are needed. The common difference is found by subtracting a term from the

The nth term is given by

The nth term is given by a_n = a + (n - 1) d. This formula gives any term directly without writing all the terms before it.

The sum of the first n

The sum of the first n terms of an AP is S = n/2[2a + (n - 1) d]. If the first and last terms are known, S = n/2(a + l) is used.

The nth term can also be

The nth term can also be written as a_n = S_n - S_{n-1}.