A model for the number of lobsters caught per year is based on the assumption that the number of lobsters caught in a year is the average of the number caught in the two previous years.

(a) Find a recurrence relation for {Pn}, where Pn is the number of lobsters caught in year n, under the assumption for this model.

(b) Find Pn if 100000 lobsters were caught in year 1 and 300000 were caught in year 2.