Algebraic properties of generalized Fibonacci Sequence via matrix Methods

• Main Authors: Sia, Jye Ying*, Ho, Chee-Kit *, Haslinda Ibrahim,, Nazihah Ahmad,
• Format: Article
• Language: English
• Published: Medwell Journals 2016
• Subjects: QA Mathematics
• Online Access: http://eprints.sunway.edu.my/592/1/Sia%20Jye%20Ying%20Algebraic%20Properties%20of%20Generalized%20Fibonacci%20Sequence.pdf; http://eprints.sunway.edu.my/592/; http://medwelljournals.com/abstract/?doi=jeasci.2016.2396.2401

Over the past centuries, the fascination over the Fibonacci sequences and their generalizations has been shown by mathematicians and the wider scientific community. While most of the known algebraic properties of these sequences were found based on the well-known Binet formula, new discoveries seemed to have been dwarfed by the nature of the complexity of its methodology. Recently, matrix method has become a popular tool among many researchers working on Fibonacci related sequences. In this study, we investigate the generalized Fibonacci sequence by employing two different matrix methods, namely, the method of diagonalization and the method of matrix collation, making use of several generating matrices. We obtained some new algebraic properties and the sum of the generalized fibonacci sequence with different indices