An arithmetic progression (AP) is a list of numbers in which each term is obtained by adding a fixed number d to the preceding term, except the first term. The fixed number d is called the common difference.
General form of an AP. a, a + d, a + 2d, a + 3d, …
In an AP with first term a and common difference d, the nth term (or the general term) is given by an
= a + (n – 1) d
The sum of the first n terms of an AP is given by :
S = n/2 [ 2a + (n - 1)d ]
If l is the last term of the finite AP, say the nth term, then the sum of all terms of the AP is given by :
S = n/2 [ a + l ]