Answer to Question #228202 in Discrete Mathematics for Chel

Question

2fn-f(n-2) = fn+1 for n>3

Answer 1

The recursive definition for generating Fibonacci numbers and the Fibonacci sequence is:

$$f_n = f_{n-1} + f_{n-2} \ where\ n\geq3$$

Then

$$f_{n+1} = f_{n} + f_{n-1}$$

$$f_{n-1}=f_{n+1}-f_{n}$$

Substitute

$$f_n = f_{n-1} + f_{n-2}=f_{n+1}-f_{n}+ f_{n-2}$$

Therefore

$$2f_n-f_{n-2} =f_{n+1}, n\geq3,\ True$$