Question

The sum of the first n terms of an AP is 2n2+5n, then its nth term is

Answer 1

Answer:-

Given:

Sum of first n terms of an AP = 2n² + 5n

Substitute n = 1 to find the first term of the AP [ ∵ sum of first 1 terms is nothing but the first term. ]

Hence,

→ a(1) = a = 2(1)² + 5(1)

→ a(1) = a = 2 + 5

→ a = 7

We know that,

Sum of first n terms of an AP = n/2 * [ a + a(n) ]

[ a(n) is the nth term ].

Hence,

→ n/2 * [ 7 + a(n) ] = 2n² + 5n

→ 7 + a(n) = n (2n + 5) * 2/n

→ a(n) + 7 = 4n + 10

→ a(n) = 4n + 10 - 7

→ a(n) = 4n + 3

∵ The nth term of the given AP is 4n + 3.