Number 2 b)

1. 10 points Give the values of, as for the following recurrences. (b) an-_ 2nan-1 + an-2, ao 3, a,-2 (c) an -2an-1 +3an-2, ao 4, a1-5 (d) an = an-1 + 2, ao = 2 (e) an (an-1)2 + an-3, a 2,a5 (f) a,-an-2, a,-0, a,-10 2. 14 points (Rosen 8.2.4) Solve these recurrence relations together with the initial conditions given. (d) an an-2, ao- 5, a1--1 3. 6 points (Rosen 8.2.8) 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 (Ln) where Ln is the number of lobsters caught in year n under th assumptions of this model. (b) Find Ln if 100,000 lobsters were caught in year 1 and 300,000 were caught in year 2