The sequence {bn} is defined by b1 = 2, b2 = 8, b3 = 8bn-1 - 7bn-2 (n ≥ 3). Find b3 and b4 and guess a formula for bn. Use induction to prove your conjecture.

The first part of this is easy, b3 and b4 being 50 and 344 respectively, but what I am having trouble with is guessing a general formula and I was wondering if anybody could help me. I know how to prove it but I don't have anything to prove yet! Thanks a lot