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

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If the sum of n terms of an A.P. is (pn + qn2), where p and q are constants, find the common difference.

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Solution:

It is known that,

According to the given condition,

Comparing the coefficients of n 2 on both sides, we obtain

=> d = 2 q

Thus, the common difference of the A.P. is 2q.

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