why does the gap between the energy levels of a hydrogen atom keep decreasing as we move further and further away from nucleus?
Whatever the radius, the allowed energy levels are proportional to $1/n^2$.
The first gap is proportional to $1/1^2 - 1/2^2 = 0.75$.
The second gap is proportional to $1/2^2 - 1/3^2 = 1/4 - 1/9 = 5/36 = 0.139$. This is smaller than $0.75$.
The third gap is proportional to $1/9 - 1/36 = 1/12 = 0.083$. It is still smaller.