"Let $X = (X_{n})_{n \geq 0}$ be a Markov chain and and let $(n_r)_{r \geq 0}$ be an unbounded increasing sequence of positive integers. Show that $Y_r = X_{n_r}$ defines a (possibly inhomogeneous) Markov chain."
I tried using the usual Markov condition and filling in the gaps by inserting the missing $X_i$ and summing, but I'm not quite sure what it is I even have to sum over.