# Deriving a Formula in Solving Reverse Fibonacci Means

## Authors

• Steven Elizalde North Eastern Mindanao State University, Surigao del Sur, Philippines
• Romeo Patan North Eastern Mindanao State University, Surigao del Sur, Philippines

## Keywords:

fibonacci sequence , reverse fibonacci sequence, Binet’s formula, means

## Abstract

Reverse Fibonacci sequence $\{J_n\}$ is defined by the relation $J_n = 8(J_{n-1} - J_{n-2})$ for $n\geq2$ with $J_0=0$ and $J_1=1$ as initial terms. A few formulas have been derived for solving the missing terms of a sequence in books and mathematical journals, but not for the reverse Fibonacci sequence. Thus, this paper derived a formula that deductively solves the first missing term $\{x_1\}$ of the reverse Fibonacci sequence and is given by the equation

$x_1=\frac{b+8aJ_n}{J_{n+1}}$.

By using the derived formula for $\{x_1\}$, it is now possible to solve the means of the reverse Fibonacci sequence as well as solving the sequence itself.

## References

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2022-12-30

## How to Cite

Elizalde, S., & Patan, R. (2022). Deriving a Formula in Solving Reverse Fibonacci Means. Recoletos Multidisciplinary Research Journal, 10(2), 41–45. https://doi.org/10.32871/rmrj2210.02.03

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