Copying entries from multiple sheets to new sheet, then summing

I run a weekly pub trivia and I use a spreadsheet to keep track of cumulative scores.

There are 6 sheets in the file...
Week 1
Week 2
Week 3
Week 4
Week 5
Cumulative.

Week 1 through Week 5 has a columns...
Team Name
Round 1
Round 2
Round 3
Round 4
Round 5
Round 6
Total

Sheet 'Cumulative' has columns
Team Name
Week 1
Week 2
Week 3
Week 4
Week 5
Total

What I'm trying to figure out is, and what I want to do is...
A). Copy all unique team names from sheets 'Week 1' through 'Week 5' to the 'Team Name' column of the 'Cumulative' sheet.

B). VLOOKUP (or something comparable) the values from the 'Total' columns of Week 1 through Week 5 of the associated Team Name to the 'Cumulative' sheet, for the associated week... as a extra caveat, if a team didn't play on a given week, ideally a zero would be displayed, if it wouldn't do that already.

C). Sum those values in the 'Cumulative' sheet. (I can do this, just trying to be thorough).

Attached are screenshots of what Week 1 and Week 2 might look like, and a manually entered version of what I'm trying to happen for the 'Cumulative' sheet. Any ideas?

Thanks in advance for any input.