Determine the solution for the recurrence relation bn=8bn-1−12bn-2with b0=3 and b1=4.
A. 7/2*2n−1/2*6n
B. 2/3*7n-5*4n
C. 4!*6n
D. 2/8n
Answer:A
Determine the solution for the recurrence relation bn=8bn-1−12bn-2with b0=3 and b1=4.
A. 7/2*2n−1/2*6n
 B. 2/3*7n-5*4n
 C. 4!*6n
 D. 2/8n

Explanation: Rewrite the recurrence relation bn-8bn-1+12bn-2=0. Now from the characteristic equation: x2−8x+12=0 we have x: (x−2)(x−6)=0, so x=2 and x=6 are the characteristic roots. Therefore the solution to the recurrence relation will have the form: bn=b2n+c6n. To find b and c, set n=0 and n=1 to get a system of two equations with two unknowns: 3=b20+c60=b+c, and 4=b21+c61=2b+6c. Solving this system gives c=-1/2 and b=7/2. So the solution to the recurrence relation is, bn=7/2*2n−1/2*6n.
