Binet's Formula for Negative Fibonacci Sequences

169 Views Asked by At

I have recently learnt the Binet's formula for calculating Fibonacci Sequences and got my mind blown.

$F_n = \frac{(1+\sqrt{5})^n-(1-\sqrt{5})^n}{2^n \sqrt{5}}$

This has worked charm for positive numbers, however I am wondering if this could be applied to the negative Sequences as well. Here is an example:

Correct me if I am wrong, but this should be the Fib Series in General right:?

Fib(n) =  -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 ...
FibValue= -8 -5 -3 -2 -1 -1 0 1 1 2 3 5 8 ...