DETERMINATION OF FIBONACCI SEQUENCE TERMS THROUGH TWO COMPUTATIONAL ALGORITHMS

Abstract

The Fibonacci sequence arose from the following problem: A pair of newborn rabbits was placed in a fenced place. Determine how many rabbit pairs they will have after one year, assuming that each month one pair of rabbits produces another pair and that each pair begins to breed two months after their birth. From this problem the Fibonacci sequence we know was built. When we build the sequence, we see that the number of rabbits increases a lot over time. In this way, it is laborious to calculate the number of rabbits when increasing the number of months. Hence, the following question arises: how many rabbits will they have after n months? For this, two computational algorithms will be built in VisuAlg: one algorithm to determine the first n terms of the Fibonacci sequence and another to determine the nth term of the Fibonacci sequence using Binet's formula.  The general objective of the work is to present a computational algorithm to determine the first n terms of the sequence. The specific objectives of the work are: to present the motivating problem of the Fibonacci sequence;  display the Fibonacci sequence as a recurrence and establish a formula for determining the terms of such a sequence. First, a bibliographic research was carried out that had as its source the books of Hefez (2016), Alencar (1981) and Burton (2010) and the article by Silva (2020).  Then, the computational algorithms were built in VisuAlg. Finally, some considerations were made, briefly showing the difficulties faced in the research and a reflection on the methodology used.