MathNet 2020 — Math Olympiad Vault — Part 05 Question 42

The geometric progressions $a_1,a_2,a_3,\ldots$ and $b_1,b_2,b_3,\ldots$ have the same common ratio, with $a_1=27$, $b_1=99$, and $a_{15}=b_{11}$. Find $a_9$.