QUADRATIC EQUATION x2 − x − 1 = 0 AND LUCAS AND FIBONACCI SEQUENCES WITH EMPHASIS ON SEQUENCES IN SCHOOL TEXTBOOKS

Document Type : Collected Paper

Author

• Hojatollah Laeli Dastjerdi

Department of Mathematics Education, Farhangian University, PO Box 889-14665, Tehran, Iran

10.22067/tmsj.2024.88602.1058

Abstract

In this article, we will examine some points related to sequences in school textbooks. By examining the school and university textbooks, it can be seen that the sequences are presented in the textbooks very briefly, which has caused students to face problems in the university. Because there are many topics such as limit, continuity, derivative and integral, existence of limit or continuity or not of some functions, and even other topics in discrete mathematics or geometry books to know the concept and characteristics of sequences. In addition, there are many sequences, each of which, depending on whether they are convergent or divergent, have interesting features that can be useful for teaching. In this article, considering the roots of an equation in the second dimension, we will introduce and examine the Lucas and Fibonacci sequences. In the following, we will discuss the characteristics of this biped and check their relationship with each other.

Keywords

• Equation
• sequence
• Lucas
• Fibonacci
• Matrix

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