### On Generalized Fibonacci like Sequence Containing Higher Powers

#### Abstract

In mathematical terms, sequence is a list of numbers arranged in a specific order. Fibonacci sequence [3] is sequence of whole numbers defined by the recurrence formula F_{n}=F_{n-1} + F_{n+2}, n>=2 and F_{0}=0, F_{1}=1 where F_{n} is an n^{th }number of sequence. Fibonacci numbers and their generalization have many interesting and surprising properties. Many authors have defined Fibonacci pattern-based sequences which are popularized and known as Fibonacci-Like sequences. When the first two terms of the Fibonacci sequence become arbitrary, it is known as Fibonacci-like sequence. Fibonacci-like sequence can start at any desired number. This study aimed to derive and validate a formula in solving Fibonacci-like sequence. Here we introduced a generalized Fibonacci Like sequence defined by G_{n+1} + bG_{n-1}, n>=1 and G_{0}=0, G_{1}=s where a, b and s are real numbers. In this research paper we introduced and derived various analytical properties. These identities of Generalized Fibonacci like sequence containing higher powers have been proved by Binet’s formula and other techniques.

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PDF#### References

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**MAYFEB Journal of Mathematics**

**Toronto, Ontario, Canada**

**MAYFEB TECHNOLOGY DEVELOPMENT**

**ISSN**

**2371-6193**