1. The problem statement, all variables and given/known data: I am just learning recurrence relations, and they are proving challenging. 2. Relevant equations -- Let's have xn = 3xn-1 + 6xn-2. I wanted to look at it with two scenarios. The first is x0 = 1 and x1 = 3. The second is x1=3 and x2 = 4 3. The attempt at a solution Is there a difference between having a staring point of x0and x1? That is the sticking point. As far as the solution is concerned, if I wanted to go to the 5th term, I can do the x1=3 and x2 = 4 scenario -- x1 = 1, x2 = 4, x3 = x3=30, x4 = 114, and x5= 522. The scenario with x0 is challenging to me. How can you have a recurrence relation where the n-1 term leaves you a negative number? How do you know where to start? Is it understood that, in the equation that is above, I would start with 3(x0(or 3 * 1) + 6(x1(6 * 3), with a sum of 21? Also, how would you turn this into a formula? How do you determine the degree? For this last question, I just need a point in the right direction, I'm not asking for someone to do the questions for me.