If the sum of $n$ terms of an A.P. is $n A + n^{2} B$ , where $A, B$ are constants, then its common difference will be

A - B

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A + B

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2 A

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2 B

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Solution

The correct option is A $2 B$
Sum = $A n + B n^{2}$
$S_{1} = A + B$
$S_{2} = 2 A + 4 A$
$S_{3} = 3 A + 9 A$
$a_{1} = A + B$
$a_{2} = S_{2} - S_{1} = A + 3 B$
$d = a_{2} - a_{1} = 3 B - B = 2 B$

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