Four numbers are in an AP. Their sum is 28, and the sum of their squares is 216. Find the numbers.

Step 1. The sum. $4a = 28$, so $a = 7$.

Step 2. The squares. $4a^2 + 20d^2 = 216$, so $196 + 20d^2 = 216$ and $d^2 = 1$.

Step 3. The numbers. With $d = 1$: $4, 6, 8, 10$. With $d = -1$ the same numbers come in reverse order.