Have you read that : Markov chain - Wikipedia, the free encyclopedia ???
What do you call open and closed ? I know transient, absorbing and recurrent... (Markov chain - Wikipedia, the free encyclopedia)
And all are transient except 2, which is absorbing, because once you're in 2, you can't leave it since it returns to itself with probability 1.
Following from the criterion for the period of a chain, I'd advise you to consider i=2. And you should conclude with ease, it's not very hard