Higher order arithmetic sequences and applications

In everyday life it is common to deal with some situations that involve the need to determine a general rule to describe them. To help in the description of phenomena that involve quantities that can be expressed in terms of polynomial functions, there is a need to find instruments that facilitate obtaining such polynomial functions from the data analyzed in the process. An easy way to obtain polynomial functions from a sequence of real numbers is through the study of Higher Order Arithmetic Sequences. If the sequence obtained from the data collected through an experiment is polynomial, then this sequence is called an arithmetic sequence of order k, where k is the degree of the polynomial. With the study of higher order arithmetic sequences it is possible to obtain from a sequence of real numbers both the formula that describes this sequence and the formula for the sum of the first n terms of this sequence. With this, we will be able to obtain general formulas that allow us to obtain an estimate for the behavior of different phenomena. Thus, through the bibliographic survey, consulting the reference [1], the research project began with weekly meetings.