Higher Order Arithmetic Progressions and Linear Recurrences
DOI:
https://doi.org/10.35819/remat2020v6i1id3700Keywords:
Arithmetic Progression, PA of Higher Order, Linear Recurrences, PolynomialsAbstract
In this article we present some relationships between higher order arithmetic progressions and linear recurrences with constant coefficients. In particular, we present a new proof using the linear recurrences of a classic result that relates the arithmetic progressions of a higher order to the polynomials. According to this proof, the general term of a sequence is a polynomial of degree k if, and only if, that sequence is an arithmetic progression of order k.
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