Estudo de sequências recursivas aplicadas ao ensino médio

Abstract

In this paper, we studied some recurrence problems which are studied at high school level, whether in high school textbook exercises, college entrance exams, selective exams or competitions. We studied with a focus on differentiating the characteristics of these sequences, seeking to obtain recurrence equations associated with each one. We found their math formulas for the nth term. We demonstrated them by finite induction and finally we applied the mathematical formulas to solve the problems studied. The organization of work is done in chapters arranged as follows: in the first chapter, we described a little about the importance of mathematics and recursive sequences for the cognitive improvement of teachers and students. In the second chapter, we cited the main definitions and properties regarding sequences, the finite induction process, and combinatorial analysis; that are necessary for the development of the work. In the third chapter, we studied some recurrence problems studied at the medium level, such as the Tower of Hanoi, Chaotic Permutation, the Fibonacci Sequence, Steiner’s Pizza and Cheese; among others. Finally, on chapter four, we described the methodology used in that work and in the fifth chapter, we made the final considerations.