Question

If the sum of n terms of an A.P.is 3n²  + 5n and its m^th term is 164, find the value of m.

Answer 1

Given S_n =3n²  + 5n ………..(1) 

and a_m = m^th term = 164 

⇒ 164 = a + (m – 1)d ………………… (2) 

Substitute n = 1, 2 in (1), we get 

S₁ = 3(1)²  + 5(1) = 3 + 5 = 8 and 

S₂ = 3(2)²  +5(2) = 12+ 10 = 22 

We know that, S₁ = first term = a and S₂ = Sum of first two terms. 

∴ S₁ = 8 = a and a + (a + d) = 22 

∴ <3 = 8 and 8 + (8 + d) = 22 

⇒ d = 6 

Substituting the values of a and d in (2), we get 164 = 8 + (m - 1)(6) 

= 8 + 6m - 6 = 2 + 6m

⇒ 162 = 6m  ⇒ m = 162/6 = 27