I am looking for a closed form equation for finding the starting values in a Fibonacci series given two consecutive numbers in this series. I found the identities $f_n = F_{n-1}a+F_nb$, where $a$ and $b$ are the starting values, and $F_n = \frac{\phi^n-\bar{\phi}^n}{\sqrt{5}}$, but I don't know what to do with this information now that I have it. I just know I need to solve for $a$ and $b$. Can anyone point me in the right direction?
2026-03-25 08:10:55.1774426255
Closed Form Equation for Finding Roots of Fibonacci Series Given Any Two Consecutive Numbers in that Series
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