Writing a bash for-loop with a variable top-end

I frequently write for-loops in bash with the well-known syntax:

for i in {1..10}  [...]

Now, I'm trying to write one where the top is defined by a variable:

TOP=10
for i in {1..$TOP} [...]

I've tried a variety of parens, curly-brackets, evaluations, etc, and typically get back an error "bad substitution".

How can I write my for-loop so that the limit depends on a variable instead of a hard-coded value?