How many terms of 5, 9, 13, … must be taken so that their sum is 275?

Step 1. The sum. $S_n = \dfrac{n}{2}[10 + 4(n - 1)] = n(2n + 3)$.

Step 2. The equation. $2n^2 + 3n - 275 = 0$.

Step 3. Solve. $D = 9 + 2200 = 2209 = 47^2$, so $n = \dfrac{-3 \pm 47}{4}$, giving $11$ or $-12.5$.

Step 4. Choose and check. $n = 11$, and $11 \times 25 = 275$.