Philippine E-Journals

Deriving a Formula in Solving Reverse Fibonacci Means

Steven L. Elizalde | Romeo A. Patan

 

Abstract:

Reverse Fibonacci sequence is defined by the recurrence relation of Jn = 8(Jn-1 – Jn-2) for n?2 with Jo =0 and J1 = 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 of the reverse Fibonacci sequence and is given by the equation By using the derived formula for x1, it is now possible to solve the means of the reverse Fibonacci sequence as well as solving the sequence itself.