Question: How can I build an increasing list using a loop

How can I build an increasing list using a loop?

Something like this

a[1]:= [...]
a[2]:= [...]
a[3]:= [...]

c[1]:=a[1]
c[2]:=[op(a[1]),op(a[2])]
c[3]:=[op(a[1]),op(a[2]),op(a[3])]

etc...

I thought about using a loop but then got stuck

for i from 1 to 3 do
  c[i]:= ???

Please Wait...