Exploring the Properties of m-bonacci Sequences

Abstract

This paper formalized the definition of an m-bonacci sequence, a generalization of the more commonly known Fibonacci and Tribonacci sequences. Four theorems are then introduced to discuss the properties of these sequences and establish a relationship between the terms of the sequence with the related characteristic equation. A generating function is obtained that expresses all the terms of the sequence, and with an elaborate analysis of the function the last theorem-to limit the ratio of consecutive terms to 2-is proved using an alternate method.