Exploring Progressions: A Collection of Problems

TL;DR

This paper provides a comprehensive exploration of various mathematical progressions, including new challenging problems and solutions, aimed at educators and specialists interested in advanced sequence topics.

Contribution

It introduces a collection of novel challenging problems and detailed solutions on progressions, including material not typically covered in standard texts.

Findings

21 challenging problems with solutions

Unsolved problems for further research

Extended material beyond standard textbooks

Abstract

The material of this work is aimed at mathematics educators, as well as math specialists with a keen interest in progressions. In this paper, we study the subject of arithmetic, geometric, mixed, and harmonic progressions or sequences. Some of the material found in Sections 2,3,4,and 5, can also be found in standard precalculus texts. For example, refer to the books in references 1 and 2. A substantial portion of the material in those sections, cannot be found in such books. In Section 6, we present 21 problems with detailed solutions. These are interesting, unusual problems not commonly found in mathematics texts, and most of them are quite challenging. In Section 7, we offer a collection of unsolved problems.