The sum of the first $n$ terms of an AP is $S_n=5n^2-3n$. Find its 8th term.

Use $a_n=S_n-S$_{n-1}. $S_8=5(64)-24=296$ and $S_7=5(49)-21=224$, so $a_8=296-224=72$. The value 62 is $a_7$, an off-by-one in the subtraction; 296 is $S_8$ itself, the total of eight terms rather than one term; 82 is $a_9$.