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 $x + y$?
This problem involves a geometric sequence, where each term is obtained by multiplying the previous term by a constant ratio. To find the ratio, I can divide any term by the previous term. For example, $81/243 = 1/3$. This means that the ratio is $1/3$, and I can use it to find $x$ and $y$. To find $x$, I multiply $81$ by $1/3$, which gives $27$. To find $y$, I multiply $x$ by $1/3$, which gives $9$. Therefore, $x + y = 27 + 9 = 36$. 