An arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term.
This fixed number is called the common difference of the AP. It can be positive, negative or zero.
The general form of an AP is a, a + d, a + 2d, a + 3d, ...
A given list of numbers a1, a2, a3, ... is an AP, if the differences a2 - a1, a3 - a2, a4 - a3, ... give the same value, , i.e., if ak+1 - ak is the same for different values of k.
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)