Math, asked by atheeqbaithadka5, 11 hours ago

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​

Answers

Answered by pratiksingbal2006
25

Answer:

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

Answered by soniatiwari214
0

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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