Sn, the sum to n terms of the GP is a+ar+ar^2+...+ar^n=a(1+r+r^2+...+r^n). rSn=a(r+r^2+r^3+...+r^n+r^(n+1)). Therefore, rSn-Sn=Sn(r-1)=a(r^(n+1)-1), so Sn=a(r^(n+1)-1)/(r-1) or a(1-r^(n+1))/(1-r), where a is the first term.
If r=-1/4 and Sn=20, 20=a(1-0.25^(n+1))/0.75; a(1-0.25^(n+1))=15. As n approaches infinity, the fraction in the numerator approaches zero, so a=15.