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

Given: Sum of n terms of A.P. = pn + qn2

We know,

where, n = nth term
a = first term and
d = common difference
Now equating the given Sum with the formula we get,

Comparing the coefficients of n2 on both sides, we obtain

d = 2q

∴ the common difference of the A.P. is 2q.

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