Simple, \[x_{n+1} - y_{n+1} = (1/2)(x_{n} - y_{n})\], and since \[(x_{n} - y_{n}) = 1/2 * (x_{n-1} - y_{n-1})\], \[x_{n+1} - y_{n+1} = (1/2)(x_{n} - y_{n}) = 1/2* 1/2 * (x_{n-1} - y_{n-1}) = 1/4 * (x_{n-1} - y_{n-1} \], and so on. Got the idea?

Salahuddin

Maths online