International Research Journal of Education and Technology

In this paper, we analyzed a new generalization of the Fibonacci sequence that leads to the copper ratio, which we term the copper Fibonacci sequence. Motivated by this definition, we also formulated the corresponding copper Lucas sequence and established several relationships between the terms of these sequences. Various properties were investigated, including explicit Binet-type formulas, special summation identities, and generating functions. Furthermore, we analyzed the roots of the associated characteristic equations and demonstrated how these roots are related to the sequence terms. Finally, we derived important identities for these sequences, including Cassini- and Catalan-type identities.

KEYWORDS

          Fibonacci sequence, Lucas Sequence, Binet formula, Copper ratio.