How many terms of 21, 18, 15, … must be added to get 81? Explain why there are two answers.

Step 1. The equation. $\dfrac{n(45 - 3n)}{2} = 81$, so $3n^2 - 45n + 162 = 0$, that is $n^2 - 15n + 54 = 0$.

Step 2. Solve. $(n - 6)(n - 9) = 0$, so $n = 6$ or $n = 9$.

Step 3. Why both. Terms $7$, $8$ and $9$ are $3$, $0$ and $-3$. They add up to $0$, so the sum after $9$ terms is the same as after $6$.