The numbers $3, x, y, 24$ are consecutive terms of a geometric progression. Find the values of $x$ and $y$.

From first term to fourth term the ratio is applied three times: $3r^3 = 24$, so $r^3 = 8$ and $r = 2$. Then $x = 3 \times 2 = 6$ and $y = 6 \times 2 = 12$. The pairs $(9, 15)$ and $(10, 17)$ come from wrongly treating the sequence as arithmetic.