Determine the solution for the recurrence relation an = 6an-1−8an-2 provided initial conditions a0=3 and a1=5.
A. an = 4 * 2n – 3n
B. an = 3 * 7n – 5*3n
C. an = 5 * 7n
D. an = 3! * 5n
Answer:B
Determine the solution for the recurrence relation an = 6an-1−8an-2 provided initial conditions a0=3 and a1=5.
A. an = 4 * 2n – 3n
 B. an = 3 * 7n – 5*3n
 C. an = 5 * 7n
 D. an = 3! * 5n

Explanation: The characteristic polynomial is x2−6x+8. By solving the characteristic equation, x2−6x+8=0 we get x=2 and x=4, these are the characteristic roots. Therefore we know that the solution to the recurrence relation has the form an=a*2n+b*4n, for some constants a and b. Now, by using the initial conditions a0 and a1 we have: a=7/2 and b=-1/2. Therefore the solution to the recurrence relation is: an = 4 * 2n – 1*3n = 7/2 * 2n – 1/2*3n.
