Question

Find the 4th term of an AP, if the sum of first n terms is 2n² + 3n
1. 41
2. 42
3. 60
4. None of these

Answer 1

Correct Answer - Option 4 : None of these

Concept:

If series is in AP then nth term of AP = a_n = S_n - S_{(n - 1)}

Calculations:

Given series is in AP and the sum of first n terms is 2n2 + 3n

⇒ S_n =2n2 + 3n.

Then, the first term will be when n=1 in the above expression

⇒ S1 = 2 + 3 = 5

Sum of first two terms,

n = 2 , S₂ = 2 × 2² + 3 × 2 = 14

So, the second term will be 

a₂ = S₂ - S₁ = 14 - 5 = 9

Similarly, 

n = 3, S3 = 2 × 3² + 3 × 3 = 27

So, the third term will be 

a3 = S3 - S₂ = 27 - 14 = 13

Similarly, 

n = 4, S4 = 2 × 4² + 3 × 4 = 44

So, the fourth term will be 

a4 = S4 - S3 = 44 - 27 = 17

Hence, the 4th term of an AP is 17.