Solving problems with smooth sequences that are subject to local restrictions

Abstract

This article discusses the options that arise when solving problems with smooth sequences that are subject to local restrictions. It also continues the cycle of work on the study of smooth sequences and supplements the literature in the field of the study of this arithmetic property. The relevance of the current research is that the smooth sequences simulate the motion of the bodies taking into account the resistance of the medium. The methodology is in solving problems and proving theorems by calculating the formulas and building the graphs and providing the comments on them. It should be noted that when conducting a literature review about such problems and their solution, we noticed a lack of a detailed review and compactness of information. Thus, this work has a scientific novelty and, as a result, practical significance for the learning process. The paper presents a detailed description of the solutions of smooth sequences on the 1st, 2nd, 3rd differences; it also provides evidence with explanations of the theorems, gives illustrations of graphs of sequences under different conditions. The results of the study may be applicated to spaceship building and ballistics. Besides this, the article is supplemented with data in tables shown in the Appendices.