The common difference between consecutive terms in an arithmetic sequence is constant.
So, the common difference between $2^2$ and $y$ is the same as the common difference between $y$ and $2^4$.
Therefore, $y-2^2 = 2^4 - y$.
Simplifying, we have $y-4=16-y$.
Combining like terms, we get $2y=20$.
Dividing by 2, we find $y=\boxed{10}$.
The answer is: 10
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
What is the integer value of $y$ in the arithmetic sequence $2^2, y, 2^4$?

### Answer:
