Remove Files of given range in bash/shell/unix -

i have files of below name format.

test_1_452161_987654321.arc   test_1_452162_987654321.arc   test_1_452163_987654321.arc   .   .   .   test_1_452190_987654321.arc

i.e need delete 30 files in above case user give below inputs

start_file = 452161   end_file   =  452190

how delete above series files? (i new bash/shell programming tried using while loop , remove dint work seeking experts help)

my code

echo "enter start file" read start echo "enter end file" read end  i=$start j=$end  while [$i -le $j]; rm *$i*.arc ((i++)) done

replace after fourth line by

for ((i=$start; i<=$end; i++));   echo rm *_${i}_*.arc done

if looks fine, remove echo.

MOno