Students’ Mathematical Difficulties and Error Patterns in Arithmetic and Geometric Sequences and Series: A Systematic Literature Review

Abstract

This study systematically examines students’ mathematical difficulties and error patterns encountered in learning arithmetic sequences and series. Using a Systematic Literature Review (SLR) approach, the literature search was conducted through international databases (Scopus), supporting databases (Google Scholar), and manual searches to ensure comprehensive coverage of relevant studies. Following the stages of identification, screening, and eligibility assessment, a total of 14 relevant empirical articles were selected for analysis. Data from these articles were extracted and analyzed using thematic analysis, focusing on types of mathematical difficulties, students’ error patterns, contributing factors, and remediation strategies reported in the literature. The findings indicate that students’ difficulties in arithmetic sequences and series are predominantly characterized by weak conceptual understanding, difficulties in transforming contextual problems into mathematical models, and reliance on formula memorization without deep understanding. The most frequently observed error patterns include misinterpretation of problems, incorrect selection and application of formulas, procedural errors in calculations, and failure to verify solutions. The underlying causes of these difficulties are generally associated with memorization-oriented instruction, limited use of mathematical representations, and insufficient exposure to non-routine problems. These findings highlight the importance of instructional approaches that emphasize conceptual understanding, problem-solving skills, and the development of metacognitive awareness in teaching sequences and series.