Question

The sum of the first n terms of an A.P. is 3n² + 6n. Find the n^th term of this A.P.

Answer 1

Let ‘a’ be the first term and ‘d’ be the common difference 

S_n= 3n² + 6n

Frist term, a, S₁ = 3(1)² +6(1)

= 3 + 6 = 9

S₂ =3(2)² + 6(2)

a + a + d = 12 + 12

9 + 9 + d = 24

18 + d = 24 d = 6 

Therefore, a_n = a + (n – 1) d 

= 9 + (n – 1) 6 

= 6n + 3