Question

If the sum of n terms of an AP  is 3n² + 5n and its m^th term is 164. Find the value of m ?
1. 160
2. 27
3. 29
4. 56

Answer 1

Correct Answer - Option 2 : 27

Concept 

General term of an AP is given by:

a_n = S_n - S_{(n - 1)}

Calculation:

Here S_n = 3n² + 5n 

an = Sn - S(n - 1) 

After solving above equation we get 

a_n = 6n + 2 

For 1st term, put n = 1

So, a₁ = 1 = 6 × 1 + 2 = 8

For 2nd term, put n = 2

So, a₂ = 14

Now, common difference = d = a₂ - a₁ = 14 - 8 = 6

Given a_m = 164 

⇒ a + (m - 1)d = 164

⇒  8 + (m - 1 ) 6 = 164

∴ m = 27