Find the sum of all the multiples of 7 between 100 and 200.

The first multiple of 7 above 100 is 105 and the last below 200 is 196. These form an arithmetic progression with $d = 7$, and the number of terms is $\dfrac{196 - 105}{7} + 1 = 14$. The sum is $\dfrac{14}{2}(105 + 196) = 7 \times 301 = 2107$. Miscounting the terms as 13 gives 1904 with the wrong last term, or 2205 with 15 terms.