Question

Solve the recurrence relation a_n = 8a_n-1- 15a_n-2 for the initial conditions a_0 = 1; a_1 = 4:
Then …and a_10:

Answer 1

let a_n =tr^n be a sol
thenn the auxillary eq stands
as follows
r^2=8r-15
or r^2-8r+15=0
or r^2 -5r-3r+15=0
or (r-5)(r-3)=0
or r=3,5
hence a_n=k(3^n)+t(5^n)
when n=0 we have 1=k+t
when n=1 we have 4=3k+5t
solving we have t=1/2 and k=1/2
hence a_n=1/2 (3^n+5^n)
for a_10 put n=10 in the above formula