How to sum up a repeating/chained formula in Google Sheets without typing each out?

I've got a chain of formulas I need that works out to:

=((C5*A5)+(C6*A6)+(C7*A7)+(C8*A8))/A3

=((D5*A5)+(D6*A6)+(D7*A7)+(D8*A8))/A3

All the way into 100's of rows, that I then need for subsequent columns. How do I make this cleaner and not have to type out every single (C*A)+etc.... I remember seeing a function at one point, but have failed to find it again.