If the sum of n terms of an A.P. is `(p n+q n^2)` , where p and q are constants, find the common difference.

Explanation

The sum of n terms of an A.P. is ( `pn+q n 2` ).


The formula for the sum of n terms in an A.P. is given by,

`S n = n 2 [ 2a+( n−1 )d ]`


Substitute the value of S n as ( `pn+q n 2 `) in the above expression.


`pn+q n 2 = n 2 [ 2a+( n−1 )d ] pn+q n 2 = n 2 [ 2a+nd−d ] =na+ d 2 n 2 − d 2 n `
...