Reggie starts his card collection with 195 trading cards in Week 1. Each week after this, he purchases 16 more trading cards.

How many trading cards will Reggie have after Week 12?

After 12 weeks, Reggie will have purchased 16*12=<<16*12=192>>192 trading cards

He will have a total of 195+192=<<195+192=387>>387 trading cards. Answer: \boxed{387}.