A New Relation between Fibonacci and Lucas sequences for 7 - steps

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Abstract

This article discusses a relation of Fibonacci and Lucas sequenceshaving seven order. This formula is used to determine thekth term of Lucas7step. 

 This paper uses the method of Natividad and Policarpio [General Mathe-matics Notes, 7 (2013), 82–87] and applies mathematical induction to prove theformula. 

The result indicates that every variable of Lucas7step forms Fibonacci7step. It can be concluded that to determinekth term of Lucas7step can be ob-tained by summing up multiplication of the first seventh term of Lucas7step andcorresponding Fibonacci7step.