Shell script “for” loop syntax

I have gotten the following to work:

for i in {2..10}
do
    echo "output: $i"
done

It produces a bunch of lines of output: 2, output: 3, so on.

However, trying to run the following:

max=10
for i in {2..$max}
do
    echo "$i"
done

produces the following:

output: {2..10}

How can I get the compiler to realize it should treat $max as the other end of the array, and not part of a string?