What is the value of $x + y$ if the sequence $2, ~6, ~10, \ldots, ~x, ~y, ~26$ is an arithmetic sequence?
The common difference of this arithmetic sequence is $6-2=4$. Since every two consecutive terms in the arithmetic sequence differ by this value, $y=26-4=22$ and $x=26-2 \cdot 4 = 18$. Hence, $x+y=22+18=\boxed{40}$.