Problem #WSP - 000125

Problems Algebra Sequences Fibonacci
 10–14  1.0

Problem

Have you wondered if F−5 is possible? Here is how we can extend the Fibonacci sequence to the negative indices. The relation Fn+1=Fn+Fn−1 can be rewritten as Fn−1=Fn+1−Fn. We can simply define the Fibonacci sequence with negative indices with this formula. For example, F−1=F1−F0=1−0=1.

Write out F−1,F−2,…,F−10. What do you notice about the Fibonacci sequence with negative indices?