Progressão aritmética e progressão geométrica no ENEM, em vestibulares e em livros-texto: algumas aplicações observadas por análise de questões, e modos de abordagem do tema

Abstract

This research on arithmetic and geometric progressions first presents relevant theoretical content for high school education, followed by a curated selection of questions from textbooks, traditional university entrance exams, and the Brazilian National High School Exam (ENEM). The objective of this research is to show the relevance of the topic of progressions for high school education, applications, and differences between approaches in questions, by researching, selecting, and organizing different exercises from tests from various places in Brazil and from different books. For each question, the main theme (arithmetic or geometric progression), associated themes, difficulty level, aspects of the wording, presence or absence of contextualization, comparisons, and various observations are examined, while the solution is presented. The work also includes some historical aspects, the association of progressions with financial mathematics, and some skills listed in the Brazilian National Common Curriculum Base.