I assume that by "membership" you mean it is a CC subscription.
If yes: CC does not need serial number, you just need to download the CC & activate it with the Adobe ID with which you have redeemed the code.
CC mostly asks for serial number if:
1. There is no CC registered to the ID with which you had signed.
2. There are entries of Adobe in Host files of the computer.
3. The activation count has increased.
Please refer to: