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Our work focuses on the transition from high school to university in the field of calculus. In France, recursive sequences are studied as one of the classical exercises in both institutions. Their studies use different theorems and notions, such as functions, convergence, monotonicity, induction, etc. The work expected at this transition requires the development of recognition and control activities on the part of the students. We propose a new task allowing the development of such activities from a dialectic between two paradigms of analysis using the calculator. We highlight that students at the end of high school have difficulties in studying these sequences, and they do not easily develop the activities of recognition and control independently. This could cause problems in understanding recursive sequences at the beginning of university.

A classic recursive sequence calculus task at the secondary-tertiary level in France