Question

ANSWER ASAP! I will give you a like and a good review for a good

answer!
6) Solve the recurrence relation an - :-4an-1 – 4an-2,00 = 1, a, = 1 = -

Answer 1

To solve the recurrence relation, we first need to find the characteristic equation:

r^2 - 4r - 4 = 0

Using the quadratic formula, we get:

r = (4 ± √32) / 2
r = 2 ± √8

So the general solution is:

an = A(2 + √8)^n + B(2 - √8)^n

Using the initial conditions a0 = 1 and a1 = -1, we can solve for A and B:

a0 = A + B = 1
a1 = A(2 + √8) + B(2 - √8) = -1

Solving for A and B, we get:

A = (-1 - √8) / -4
B = (1 + √8) / 4

Therefore, the solution to the recurrence relation is:

an = [(-1 - √8) / -4](2 + √8)^n + [(1 + √8) / 4](2 - √8)^n

I hope this helps!