how do u solve this problem F(n+2) + F(n-2)?

Question

I been solving it but if supposed to turn out to be a fibonacci. i cant get it to turn out that way.

i fiqured it out. its 3Fn=F(n+2) + F(n-2)

Answer 1

Start off with the first few terms and prove it by induction.

F(n+2) + F(n-2) = 3F(n)


Doug

Answer 2

r u joking or are u really serious
look if F(x) = 1
then F(n+2) + F(n-2) =1 +1 =2
if F(x) = x
then F(n+2) + F(n-2) =x-2 + x+2 =2x
if F(x) =x^2
then F(n+2) + F(n-2) =(x+2)^2 + (x-2)^2 = 2x^2+8
actually u hve to tell wht is on right hand side
ur qurestion is incomplete beacause every equation must have well defined left and right handed sides ,have u read chapter on linear equations.Go and read it first.

Answer 3

One possibility - what is F(x)?
Another possibility - define F(0)

When n = 0, you have F(2) + F(-2)
When n = 2, you have F(4) + F(0)

Obviously you have quite a few unknowns to figure out.

Answer 4

Fibonacci sequence
F(1) = 1
F(2) = 1
Then F(n) = F(n-1) + F(n-2) for n > 2

Is that what you were looking for?

Answer 5

Not possible to complete. You need something on the "other side" of the equation providing a constant starting point.

Answer 6

F (n+2) + F (n-2) = F (2n)
try it for any F(n)....
any way the question is not complete
so it's a wrong answer!

Answer 7

Zero?

Answer 8

Fn+F2+Fn-F2

thus, 2(Fn)