Final answer:
The recurrence relation an = 5an-1 - 6an-2 is solved by finding the characteristic equation, determining its roots, and using the initial conditions to find the constants in the general solution, which results in an = 3*2^n - 2*3^n.
Step-by-step explanation:
The recurrence relation given is an = 5an-1 - 6an-2, with base conditions a0 = 1 and a1 = 0. To solve this, we need to find the characteristic equation, which is r^2 = 5r - 6. Solving this quadratic equation gives us the roots r = 2 and r = 3, indicating that the general solution to the recurrence relation is of the form an = A*2^n + B*3^n.
Using the base conditions, we set up two equations: 1 = A*2^0 + B*3^0 and 0 = A*2^1 + B*3^1, which simplifies to 1 = A + B and 0 = 2A + 3B. Solving these simultaneous equations, we get A = 3 and B = -2. Thus, our particular solution is an = 3*2^n - 2*3^n.