If your situation were different and you were saying that he is a serial cheater, then my answer would be different. After a one week affair, and since it's his first one, I would say that in time the uncertainty can go away under proper conditions.
He broke the trust you freely gave. Now it won't be freely given. It has to be earned back.
Marital boundaries must be firmly in place. This means the two of you fully understand what is allowed and what is not allowed, even if they have to be written out and signed by the two of you.
Transparency - No Secrets! Showing up at his work unexpectedly for lunch, for example, should be ok with him. No secret passwords. Access to online phone bill. He doesn't mind you answering his phone, using his phone, etc.
Walk a Mile In My Shoes
Married 14 yrs. Now Separated & in NC
2 grown DD's - his from previous M
4 grown kids (2DS, 2DD) mine from previous M