Generalized Fibonacci – Lucas sequence its Properties

Abstract

S equences have been fascinating topic for mathematicians for centuries. The Fibonacci sequences are a source of many nice and interesting identities . A similar interpretation exists for Lucas sequence. The Fibonacci number, Lucas numbers and their generalization have many interesting properties and applications to almost every field. Fibonacci sequence is defined by the recurrence formula and , where are an n th number of sequences. The Lucas Sequence is defined by the recurrence formula and , where an nth number of sequences are. In this paper, we present generalized Fibonacci-Lucas sequence that is defined by the recurrence relation , with B0= 2s, B1 = s . We present some standard identities and determinant identities of generalized Fibonacci-Lucas sequences by Binets formula and other simple methods. Keywords : Fibonacci sequence, Lucas Sequence, Generalized Fibonacci sequence, Binets Formula.