Numerical sequences are one of the mathematical subjects linked to everyday life, and are taught at several levels in Morocco. However, many students still had difficulty teaching this subject, more specifically the limits of numerical sequences and the nature of convergence. The aim of this study was to analyse the learning difficulties of students in the 2nd year of the baccalaureate, experimental sciences series in Morocco. To this end, a written test consisting of 6 questions relating to the notion of convergence of a numerical sequence was administered to 60 students, followed by a questionnaire sent to mathematics teachers at the qualifying secondary level. The results show that the learning difficulties associated with this concept are of several kinds: didactic, pedagogical and epistemological. Using the "Teaching at the Right Level" approach (TARL), teachers can help learners overcome the learning difficulties of numerical sequence convergence by providing support tailored to their individual needs. This promotes progress that is more effective and a better understanding of mathematical concepts. This can help students overcome learning barriers by offering varied teaching aids and promoting a better understanding of the concepts of convergence of numerical sequences.