Question

if nth term of an AP is (2n+1) find the sum of first n terms of A.P.

Answer 1

if nth term is (2n+1) so first term is 3
so,
Sn = n/2(a+an) = n/2 (3+2n+1) = n/2 (2n+4) = n(n+2)

Answer 2

Answer:

Given :

nth term = 2 n + 1

= > a₁ = 2 + 1

=  3

= > a₂ = 4 + 1

= 5

d = a₂ - a₁

= > 5 - 3

= 2

Sₙ = n / 2 [ 2 a + ( n - 1 ) d ]

Sₙ = n / 2 [ 6 + ( n -1 )  2 ]

Sₙ = n / 2 [ 6 + 2 n - 2 ]

Sₙ = n / 2 × [ 4 + 2 n ]

Sₙ =n ( n +  2 )  .

Therefore , sum of first n term is n ( n + 2 ) .