Question

consider the following recurrence relation
P(n) = 5P(n-1) - 6P(n-2) if n> 0 and P(1) = 3, P(2)=7 COMPUTE P(N) FOR N=3,4,5,6,7
no idea how to start, Discrete mathematics

Answer 1

x2-5x+6=0 -> x=-1 , 6
P(n)=a(-1)^n+b6^n
P(1)=-a+6b=3
P(2)=a+36b=7
b=5/21
a=30/21-3=-33/21
P(n)=1/21(-33(-1)^n+5.6^n)
n=3,4,...