If the sum of p terms of an A.P is 3p ²+ 4p, find its n ^thterm.

Given: S _p = 3p ² + 4p

For n,

S _n = 3n ² + 4n

For n – 1,

S _n-1 = 3(n – 1) ² + 4(n – 1)

T _n = S _n - S _n-1
⇒ T _n = (3n ² + 4n) – [3(n - 1) ² + 4(n - 1)]
⇒ T _n = (3n ² + 4n) – [3(n ² – 2n + 1) + 4(n - 1)]
⇒ T _n = (3n ² + 4n) – [3n ² – 6n + 3 + 4n - 4]
⇒ T _n = (3n ² + 4n) – [3n ² – 2n - 1]
⇒ T _n = 3n ² + 4n – 3n ² + 2n + 1
⇒ T _n = 6n + 1

Therefore the n ^th term is 6n + 1.