Question

The sum of n term of an AP is 5n-n^2 .find the nth term of this AP

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

an = a + (n − 1)d

= 4 + (n − 1) (−2)

= 4 − 2n + 2

= 6 − 2n.

∴ nth term of an A.P = 6 - 2n.