Progressions

An arithmetic progression is a list

An arithmetic progression is a list of numbers in which each term after the first is obtained by adding a fixed number. The general form is a, a + d,

The fixed number added to each

The fixed number added to each term in an arithmetic progression is called the common difference. It is found by subtracting one consecutive term from

The nth term of an AP

The nth term of an AP with first term a and common difference d is a_n = a + (n - 1)d.

The sum of first n terms

The sum of first n terms of an AP is S_n = n/2 [2a + (n - 1)d] or S_n = n/2 (a + l), where l is the last term.

The nth term of an AP

The nth term of an AP is the difference of two consecutive partial sums: a_n = S_n - S_(n-1).