Question

The first term and the last term of an arithmetic progression are ‘a’ and ‘l’

respectively, then the sum of its first ‘n’ terms is​

Answer 1

Answer:

sum of first n terms =n/2 (a+l)

Answer 2

Concept:

Arithmetic Progression (AP) can be defined as a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value known as a common difference.

Given:

The first term and the last term of an arithmetic progression are given as ‘a’ and ‘l’ respectively.

Find:

The sum of first n terms.

Solution:

The Sum of n numbers in an arithmetic progression is defined as,

S = (n/2) [2a+ (n-1)d]

where S is the sum of the terms of arithmetic progression, n is the number of terms, a is the first term and d is a common difference.

The nth term of an arithmetic progression,

aₙ = a+ (n-1)d

Here, the nth term is the last term.

So, l = a+ (n-1)d

The Sum of n numbers in an arithmetic progression can be modified as

S = (n/2) [a+ a+ (n-1)d]

S = (n/2) [a+l ]

Hence, the sum of its first ‘n’ terms of an arithmetic progression will be (n/2) [a+l ] where a and l are the first and last terms of an arithmetic progression respectively.

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