Each successive term in the sequence $2048, 512, 128, x,
y, 2, \frac 12, \frac 18,...$ is obtained by multiplying the previous term by a constant. What is the value of $x + y$?
This is a geometric sequence, where each term is obtained by multiplying the previous term by a constant ratio. I can find the ratio by dividing any term by the previous term. For example, $\frac{512}{2048} = \frac 14$, so the ratio is $\frac 14$. This means that to get the next term, I multiply the current term by $\frac 14$. So, to find $x$, I multiply $128$ by $\frac 14$, and get $x = 32$. To find $y$, I multiply $x$ by $\frac 14$, and get $y = 8$. Therefore, $x + y = 32 + 8 = 40$. 