An AP is described only by its sum function $S_n=4n^2+2n$.
Using it, work out the total of the 5th through 9th terms.

Terms 5 to 9 together make up $S_9-S_4$. Here $S_9=4(81)+18=342$ and $S_4=4(16)+8=72$, so the total is 342 - 72 = 270. Subtracting $S_5=110$ instead of $S_4$ gives 232, which wrongly removes the 5th term as well. 342 is $S_9$, the total of all nine terms, and 110 is $S_5$.