Question

The sum of the first n terms of an AP is (3n²+6n) . Find the nth term and the 15^th term of this AP. 

Answer 1

Let  S_n denotes the sum of first n terms of the AP. 

∴ s_n  = 3n² + 6n

⇒ `s_(n-1 )= 3 (n-1)^2 + 6 (n-1)`

= 3 ( n²  - 2n + 1) + 6 (n-1) 

= 3n² - 3

∴ n^th  term of the AP , a_n 

= s_n  = s_n-1 

= (3n² + 6n) - ( 3n² -3)

= 6n + 3 

Putting n=15,we get

a₁₅ = 6 × 15 + 3 = 90 + 3 = 93

Hence, the  n^th  term is (6n + 3) and 15^th term is 93.