<![CDATA[This study aims to describe a learning trajectory for the topics of sequences and its limits in Real Analysis that connects abstract mathematical concepts with school mathematics. The research employed a Design Research approach consisting of three stages: preliminary design, design experiment (including pilot and teaching experiments), and retrospective analysis. The participants were 30 fifth-semester students of the Mathematics Education Study Program at UIN Syarif Hidayatullah Jakarta. Data were collected through student worksheets, classroom observations, and interviews, and were analyzed qualitatively by comparing the Hypothetical Learning Trajectory (HLT) with the actual learning trajectory that emerged during instruction. The results indicate that the developed trajectory effectively supported students in understanding the concepts of real number sequences, convergent and divergent sequences, and limits through a gradual process from intuitive to formal understanding. Revisions to the worksheets and HLT in the second phase also improved students’ ability to generalize patterns and build mathematical connections. This study contributes to the development of a relevant Local Instruction Theory (LIT) for Real Analysis instruction in mathematics teacher education and offers an alternative instructional design that bridges the gap between school mathematics and advanced mathematics.]]>
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