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Question

What is the formula of the sum Sn of the terms of an arithmetic progression.


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Solution

Sum of arithmetic progression(A.P)

Arithmetic Progression:

A sequence of numbers that has a common difference between any two consecutive numbers is called an arithmetic progression (A.P.).

The arithmetic progression general form is given by a,a+d,a+2d,a+3d,.......

Hence, the formula to find the nth term is:

an=a+(n–1)×d

Sum of arithmetic progression(A.P).

The Sum of n terms in AP can be calculated by using the formula:

Sn=n2(2a+(n–1)d)

The Sum of all terms in a finite AP with the last term as ‘l’ can be calculated by using the formula:

Sn=n2(a+l)

Where,

n is the number of terms.
a is the first term.
d is a common difference.
l is the last term.

Hence, the sum Sn of the terms of an arithmetic progression is defined by the formula ,Sn=n22a+n–1d.


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