Let f(x)=x+1 and g be maps on R and h(n)=(g ° f)(n+1)-(g ° f)(n), n ∈ N. Further, h(1), h(2), h(3), h(4), …, is an A.P. and h(25)=53, h(101)=205. If…

Let $\displaystyle f(x)=x+1$ and $\displaystyle g$ be maps on $\displaystyle \mathbb{R}$ and $\displaystyle h(n)=(g \circ f)(n+1)-(g \circ f)(n), n \in \mathbb{N}$. Further, $\displaystyle h(1), h(2), h(3), h(4), \ldots$, is an A.P. and $\displaystyle h(25)=53, h(101)=205$. If $\displaystyle g(48)-g(2)=100 k$, then ' $\displaystyle k$ ' is equal to \_\_\_\_.