problem: Each successive term in the sequence $243, 81, x,
  y, 3, \ldots$ is obtained by multiplying the previous term by a constant. What is the value of $x + y$?
solution: The common ratio $r$, is $\frac{1}{3}$ (You can find this by dividing 81 by 243).  Therefore, $ x = 27$, $y = 9$, and $x+y = \boxed{36}$