In an A.P if sum of its first n terms is 3n^{2} + 5n and its k^{th} term is 164, find the value of k.

### Answer

Here, S_{n} = 3n^{2} + 5n

⇒ S_{1} = 3.1^{2} + 5.1 = 8 = a_{1}

S_{2} = 3.2^{2} + 5.2 = 22 = a_{1} + a_{2}

a_{2} = 22 – 8 = 14

⇒ d = 6

t_{k} = 164

⇒ 8 + (k – 1)6 = 164

⇒ k = 27