1. Suppose an = 4an-1 - 4an-2 (n 2) with a = 1 and a = 3. Find an by using the method of characteristic equations. Hint: see the example on Page 238 and in general, Theorem 7.4.2. == 2. Suppose hn hn-1 + 9hn-2 - 9hn-3 (n 3) with h = 0, h = 1, and h = 2. Find h by using the method of characteristic equations. 1+x 3. Suppose a sequence h has a generating function f(x) = Find hn. Hint: use (2+x)(1-2x) partial fractions first. Once obtaining 24x, rewriting it as a/z = =0 0(-)". 2 1+ 4. Suppose hn = hn-1 -2hn-2 (n 2) with ho = -1 and h = 1. Find the generating function of hn. Note: you do not need to do partial fraction or find hn.