rolling dices and coins problem

I have other probability problem, could anyone help me with this one?

Die A has five olive faces and one lavender face; die B has three faces of each of these colors. A fair coin is flipped once. If it falls heads, the game continues by throwing die A alone; if it falls tails, die B alone is used to continue the game. However awful their face color may be, it is known that both dice are fair.

a. Determine the probability that the nth throw of the die results in olive.

b. Determine the probability that both the nth and (n+1)st throw of the die results in olive.

c. If olive readings result from all the first n throws, determine the conditional probability of an olive outcome on the (n+1)st toss. Interpret your result for large values of n.

generalize for 'n' die tosses

How can I generalize for large values of 'n'?