Expected value of a simple Markov Chain

This is probably simple to those who know stochastic processes, but I am finding it difficult to understand how to solve expectations of a sequence.
If y(t) is a simple Markov chain where y(t) = r.y(t-1) and r is a constant, what is the unconditional expectation of the product of the last k observations y(t-k).y(t-k+1).....y(t-1).y(t)? I know how to solve it upto t-1 : E[y(t-1).y(t)] = r, but I need help in how to solve E[y(t-2).y(t-1).y(t)], for example. Would be grateful for even a lead.