Arithmetic Progression-Class X

(1) 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 is called the common difference.

The general term of an AP is

a, a + d, a + 2d, a + 3d, ……….

(2) A given list of numbers a1, a2, a3 ………………… is an AP if the differences a2 - a1, a3 – a2, a4 – a3, ………………… give the same value.

In other words, if a k+1 – ak is the same for different values of k, the term is an AP

(3) In an AP with first term a and common difference d, the nth term is given by

an = a + (n – 1)d

(4) The sum of the first n terms of an AP:

(5) 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)