Question

If S_n = n (4n + 1) is the sum of n terms of an A.P., then its common difference is ______.

Answer 1

If S_n = n (4n + 1) is the sum of n terms of an A.P., then its common difference is 8.

Explanation:

Let S_n = 4n² + n be the sum of n terms. 

The n^th term T_n = S_n – S_{n – 1} 

= [4n² + n] – [4(n – 1)² + (n – 1)] 

= 8n – 3

So T_n = a + (n – 1)d 

= 5 + (n – 1) × 8 

Hence the common difference d = 8.