A method for obtaining Fibonacci identities

TL;DR

The paper introduces a new method for deriving identities involving Fibonacci and Lucas sequences, including an interpolating identity for second-order linear recurrences, expanding tools for analyzing recurrence relations.

Contribution

It presents a novel method for generating identities for recurrence sequences, specifically providing an interpolating identity for second-order linear recurrences.

Findings

Derived new Fibonacci and Lucas identities

Proposed a general method for recurrence sequence identities

Found an interpolating identity for second-order recurrences

Abstract

For the Lucas sequence $\{U_{k}(P,Q)\}$ we discuss the identities such as the well-known Fibonacci identities. We also propose a method for obtaining identities involving recurrence sequences. With the help of which we find an interpolating type identity for second order linear recurrences.