Alternative Method for Finding Means of Fibonacci and Fibonacci-Like Sequences

Romeo A. Patan, Steven L. Elizalde

Abstract


Fibonacci sequence {Fn}  is defined as F1 = F2 = 1  and, for n ≥ 2, Fn = Fn-1 + Fn-2 . Fn , is called nth Fibonacci number. When the first two terms of the Fibonacci sequence become arbitrary, it is known as Fibonacci-like sequence. Fibonacci-like sequence can start at any desired number. Natividad introduced a method for solving means of any Fibonacci-like sequence where it starts to find the first missing term of the sequence. This study derived an alternative method for finding means of any Fibonacci-like sequence. Descriptive case-investigatory and deductive process was employed to discover the alternative method with the utilization of the existing formulas and method of solving Fibonacci means. Based on the results of the study, it was concluded that the means of any Fibonacci-like sequence can be determined using the derived  alternative method.

 


Keywords


Alternative Method; Fibonacci and Fibonacci-like Sequences; Fibonacci Means

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References


Gulec, H. H. & Taskara, N. (2009). On the properties of Fibonacci numbers with binomial coefficients. International Journal of Contemporary Mathematical Sciences, 4(25), 1251-1256.

Natividad, L. R. (2011). On solving pell means. International Journal of Mathematical Archive, 12(2), 2736-2739.

Natividad, L. R. (2012). Fibonacci means and its applications. International Journal of Mathematical Archive, 3, 1087-1090.

Rabago, J. F. T. (2012). On Natividad’s formula for solving the missing terms of a recurrence sequence. International Journal of Mathematical Archive, 8, 3105-3107.


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