My code which adds fibonacci numbers to a list adds too many terms.

[DPaul]

I just have one final question. Why is j not the final value?

I can only explain it the verbose way.
You start with "x = [0,1]", then you say "for j in x:"
So you start with 0 first, which is not the last one, but you are always adding the true last and one-but-last [-1] and [-2]
With the sum you are adding a third item, while the loop now moves to the second one.
So by testing j you are always "late".
Paul