For an AP the sum of the first $n$ terms is $S_n=\frac{n(7n-3)}{2}$. Find its common difference.

$a=S_1=\frac{1(4)}{2}=2$ and $S_2=\frac{2(11)}{2}=11$, so $a_2=S_2-S_1=9$ and $d=9-2=7$. Shortcut: writing $S_n=\frac{7}{2}$$n^2-\frac{3}{2}$$n$ in the form $A{n}^2+Bn$ gives $d=2A=7$. The option $\frac{7}{2}$ is the error of taking $d=A$ instead of $2A$; 2 is the first term a; 9 is the second term $a_2$, not the difference.