Question

If the 8th term of an A.P. is 30 and the sum of its first eight terms is 156 , find its nth term?

Answer 1

a8=30
S8=156


a + 7d =30 -----(i)
8/2[2a(8-1)×d]=156
=> 4[2a+7d]=156
=>8a+28d=156-----(ii)
divide eq(i) by 8 :-
we get,
8a+56d=240----(iii)
Subtract eqn(ii) from eqn(iii):-
8a + 56d = 240
8a + 28d = 156
(-) (-) (-)
_____________
28d = 84
d =3
putting value of 'd' in eqn(i):-
a + 7×3 = 30
a = 30-21
a = 9
an= a + (n-1)×d
=9 + (n-1)×3
=9 + 3n-3
= 6+3n
So nth term is 3n+6.