If the sum of p terms of an AP is . . .

Question : If the sum of p terms of an AP is 3p²+4p, find its nth term.

Doubt by Nimit

Solution : 

S_p = 3p²+4p
S₁=3(1)²+4(1)
S₁=3(1)+4
S₁=7

∵ S₁=a₁=a=7

∴ a =7

S₂=3(2)²+4(2)
S₂=3(4)+8
S₂=12+8
S₂=20
a₁+a₂=20
7+a₂=20
a₂=20-7
a₂=13

d=a₂-a₁
d=13-7
∴ d=6

a_n=a+(n-1)d
a_n=7+(n-1)6
a_n=7+6n-6
a_n=6n+1

Note : You could also find the nth term using the identity a_n=S_n-S_n-1