For an AP, $S_n=4n^2+n$. Find its first term and its common difference.

$a=S_1=4+1=5$. Also $S_2=16+2=18$, so $a_2=18-5=13$ and $d=13-5=8$. Shortcut: for $S_n=A{n}^2+Bn$ the common difference is $d=2A=2(4)=8$, not 4 — taking $d=A$ is the commonest error and gives the option $d=4$. "$a=4$" misreads the coefficient 4 as the first term, and "$a=8,d=5$" swaps the two answers.