Sequence or progression is a group of numbers forming a pattern. Arithmetic Progression (AP) is a progression in which each term, except the first, is obtained by adding a constant to the previous term.

A sequence is called an arithmetic progression, if there exists a constant d such that

a_{2} - a_{1} = d, a_{3} - a_{2} = d, a_{4} - a_{3} = d, and so on.

d is called the **common difference**.

**Formation of AP or General form of AP:** If a is the first term and d is the common difference, then AP is

a, a + d, a + 2d, a + 3d, a + 4d, and so on.

**n ^{th} term:** t

_{n}= a + (n - 1)d

**Sum of first n terms:** S_{n} = n/2(a + l), where

l (last term) = a + (n - 1)d, a = first term, d = common difference , n = number of terms

S_{n} = n/2[2a + (n - 1)d]

**n ^{th} term in terms of S_{n}:** t

_{n}= S

_{n}- S

_{n-1}

**Various terms of AP:** 3 consecutive terms are a - d, a, a + d and common difference is d. 4 consecutive terms are a - 3d, a - d, a + d, a + 3d and common difference is 2d.