Question

What is the formula of the sum $S_n$ of the terms of an arithmetic progression.

Answer 1

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:

$a_n=a+(n–1)\times d$

Sum of arithmetic progression(A.P).

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

$S_n=\left(\frac{n}{2}\right)(2a+(n–1\left)d\right)$

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

$S_n=\left(\frac{n}{2}\right)(a+l)$

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 $S_n$ of the terms of an arithmetic progression is defined by the formula ,$S_n=\frac{n}{2}\left(2a+\left(n–1\right)d\right)$.