Question

If the sum of n terms of an A.P. is given by S_n = 3n + 2n², then the common difference of the A.P. is
(a) 3
(b) 2
(c) 6
(d) 4

Answer 1

Let S_n denote sum of n terms of an A.P
Such that S_n = 3n + 2n²
i.e S₁ = 3(1) + 2(1)²
S₁ = 3 + 2 = 5
where S₁ = a (first term only)
S₂ = a + (a + d) where a + d represents second term and d is common difference.
$\begin{array}{rcl}{S}_2& =& 3\left(2\right)+2{\left(2\right)}^2\\ & =& 6+2\left(4\right)\\ & =& 6+8\\ S_2& =& 14\end{array}$
i.e 2a + d = 14
i.e 10 + d = 14
d = 4
i.e common difference of A.P is 4

Hence, the correct answer is option D.