It goes down a meters, then goes up ra meters, then down ra meters, then up r^2ameters, then down r^2a meters, etc. Thus we have a+2ra+2r^2a+2r^3a... or a(1+2r+2r^2...) or a +2r(1+r+r^2...). This is a+2r/(1-r).

Each iteration shades in 4(1/4)^2 =1/4 of its respective square. Each respective square is one fourth the previous square. Thus our series is 1/4+1/4^2+1/4^3+1/4^4... That is 1/4(1+1/4+1/4^2...) or 1/4(1/(3/4))=1/3