To solve this, we need to use the formula for the sum of n terms of an Arithmetic Progression (AP), which is n/2*(2a + (n - 1)d), where 'a' is the first term and 'd' is the common difference.
Given that the sum of the AP is equal to Pn + Qn², we can equate the two sums to find the value of 'd', the common difference.
Now, let's match the coefficients on each side of the equation.
2a, the coefficient of 'n' in the AP sum formula, matches with P, the coefficient of 'n' in the given equation. So, we have 2a = P.
To find 'd', we need to match the coefficient of 'n²' in both formulas. On the left side, it is (n - 1)d while on the right side it is Qn. Therefore, we can write (n - 1)d = Qn.
Now, we are asked to find the common difference 'd'. So, we rearrange the equation to solve for 'd'. After rearranging, we get d = 2*Q
Hence, after comparing the coefficients, we find that the common difference 'd' of the Arithmetic Progression is 2Q. So, the correct answer is option (a) i.e., 2Q.
Answer: a. 2Q