So you have an initial downward speed of "G" and every second "G" is added to its speed? Then it should be easy to see that the speed after n seconds is nG. Further the distance traveled in n seconds will be G+ 2G+ 3G+ ...+ nG= G(1+ 2+ 3+ ...+ n). That last is an "arithmetic sum". It is well known (and typically learned in a "precalculus" class if not in algebra) that the sum is 1+ 2+ 3+ ...+ n= n(n+1)/2.
So, if I have understood your scenario correctly, the distance the object falls in n seconds is Gn(n+1)/2. To find the time required to fall a given distance, h, solve Gn(n+1)/2= h.
n(n+1)= n^2+ n= 2h/G or n^2+ n- 2h/G= 0. You can solve that using the quadratic formula. If, as appears from what you can say, that you can only deal with integer numbers of seconds, if the solution is n.****, not an integer, then all you can say is that the time to hit the surface is between n and n+1 seconds.