I have a folder with files named as file_1.ext...file_90.ext. I can list a range of them with the following command:
file_1.ext...file_90.ext
$ ls /home/rasoul/myfolder/
The range pattern {A..B} does not accept variables for A or B. You need constants for them. A workaround might be to start a subshell like this:
{A..B}
A
B
RESULT=$(bash -c "ls {$a..$b}")