Each copy of Vegas has its own serial number. If you already have older versions with their serial numbers, you are fine. But you can't purchase a recent version and then use that serial on an older version.
@urick-p Every version (e.g. 17, 18, 19, 20, 21) of VEGAS Pro has its own specific serial number. So your VEGAS Pro 21 serial number is valid for VEGAS Pro 21. Only VEGAS Pro 21 can be activated with that serial number.