Question

The sum of first n terms of an A.P. is 5n-$n^2$. Find the nth term of this A.P.

Answer 1

Given that sum of the first n terms of an AP is 5n - n²

Sn = 5n − n²

First term, a₁ = S₁ = 5(1) − (1)² = 5 − 1 = 4

Sum of first two terms = S₂ = 5(2) − (2)² = 10 − 4 = 6.

Second term, a₂ = S₂ − S₁ = 6 − 4 = 2

d = a₂ − a₁ = 2 − 4 = −2

a_n = a + (n − 1)d

= 4 + (n − 1) (−2)

= 4 − 2n + 2

= 6 − 2n.

∴ n^th term of an A.P = 6 - 2n.