Deriving a Formula in Solving Reverse Fibonacci 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.