Is the sequence an a solution to the recurrence relation an

Is the sequence {a_n} a solution to the recurrence relation a_n = 8a_n-1 - 16a_n-2 if: a_n = 0 a_n = 1 a_n = 2^n a_n = 4^n a_n = n4^n a_n = 2 middot 4^n +3 3n middot 4^n a_n = (-4)^n a_n = n^2 4^n

Solution

Given recurrence is a linear homogeneous recurrence

So solution is of the form

a_n=r^n

SUbstituting gives

r^2=8r-16

r^2-8r+16=0

r=4

So repeated roots

HEnce general solution is

a_n=A*4^n+Bn4^n

a. 0

Yes. By setting A=B=0

b.

No.

c.

NO

d.

Yes.

Setting. A=1,B=0

e.

Yes

Set,A=0,B=1

f.

Yes

Setting., A=2,B=3

g. No

h. NO