Find the sum of all the multiples of 7 that lie between 100 and 300.

Step 1. The first and last terms. $7 \times 15 = 105$ and $7 \times 42 = 294$.

Step 2. How many. $294 = 105 + (n - 1) \times 7$, so $n - 1 = 27$ and $n = 28$.

Step 3. The sum. $S_{28} = \dfrac{28}{2}(105 + 294) = 14 \times 399 = 5586$.