The series is represented by a+ar+ar^2+r^3+.... If we call the sum of the series S then the nth term is ar^n, where n starts at 0. In our case r=2.5 and a=2. rS=ar+r^2+ar^3+...+ar^(n+1) = S+ar^(n+1)-a. Therefore S = (ar^(n+1)-a)/(r-1) = a(r^(n+1)-1)/(r-1). This is the sum up to the nth term. Putting in values for a and r and n=10, we get S=12,714.32422 if we take the meaning of the question to be n+1=10. This is option a, or rather as close to it as we've got.