Of the nth circle, in terms of r, the radius of the large green circle? Notice that the two red circles are equal, both with radius $\frac{r}{2}$
How to solve this without using René Descartes's theorem?
Problem found at page 17 of ''Problema Bonitos de Geometría con métodos elementales'' (a large pdf). Solution by René Descartes's theorem at page 44.
Can you solve the problem by Pappus Chain?