Question

If the sum of first n terms is (3n² + 5n), find its common difference.

Answer 1

Let  S_n denotes the sum of first n terms of the AP.

∴ s_n = 3n²  + 5n

⇒ `s_(n-1) = 3 (n-1) ^2 + 5 (n-1)`

= `3(n^2 - 2n + 1) + 5 (n-1)`

=`3n^2 -n-2`

Now , 

n^th term of AP , a_n = s_n -  s_n-1 

 = (3n² + 5n ) - ( 3n² -n-2) 

= 6n + 2 

 Let d be the common difference of the AP.

∴ d = a_n - a _n-1 

= (6n + 2 ) - [ 6(n-1 ) +2]

= 6n + 2 - 6 (n-1) -2

= 6 

Hence, the common difference of the AP is 6.