Question

if sum of n terms of an ap is n²+5n, then find its nth term

Answer 1

S1 = 1 + 5= 6 = a, first element
S2 = 4+10= 14 = a+second element
So second element = 14-a = 8
Similarly S3= 9+15= 24
So a3 = 24-(6+8) = 10
So the AP is 6,8,10..... Where a=6 and d=2
Therefore nth term = a+(n-1) d
So nth term = 6+(n-1)2 = 2n+4