Given an A.P. of common difference 6 and sum of n terms of the A.P. is given as $a n^{2} + b n$ where a and b are constants. Find the value of 'a'.

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Solution

The correct option is D 3
Let the first term of the given A.P. be 'a'.
Sum of n terms of an A.P. with first term 'a' and common difference 'd' $= \frac{n}{2} [2 a + (n - 1) d]$
Given common difference of the A.P = 6
Sum of 'n' terms of the given A.P $= \frac{n}{2} [2 a + (n - 1) 6] = \frac{n}{2} [2 a + 6 n - 6] = n [a + 3 n - 3] = 3 n^{2} + (a - 3) n$

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