The sum of first n terms of an AP is (3n² + 6n). The common difference of the AP is

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

Sum of first n terms = S_n = 3n² + 6n

Then n^th term is given by: a_n = S_n - S_{n - 1}

∴ a_n = (3n² + 6n) - [3(n - 1)² + 6(n - 1)]

= (3n² + 6n) - [3(n² + 1 - 2n) + 6n - 6]

= 3n² + 6n - 3n² - 3 + 6n - 6n + 6

= 3 + 6n

Now, common difference = d = a_n - a_{n - 1}

= 3 + 6n - [3 + 6(n - 1)]

= 3 + 6n - 3 - 6n + 6

= 6

∴ Common difference = 6