Geometric Sequences Filling the Gaps (Part 2)

This GeoGebra example visually demonstrates how a geometric sequence can “fill the gaps” in a geometric construction: by using a fixed ratio q, successive segment lengths or point positions are generated through proportional recursion, covering intervals that initially look missing. The key mathematical ideas are geometric sequences, the geometric mean, and the term-generation rule determined by the common ratio. Construction and interactivity rely on GeoGebra commands and objects such as RandomElement for choosing parameters, If for conditional logic, and list-based objects (rlist, a1list, a2list, a3list, qlist/qQ) to store and compute sequence-related quantities. The script defines variables (e.g., a1, a2, a3, rR, aA, ha, va), constructs several key points (P1–P7), and uses text1–text7 to label intermediate terms and relationships. Buttons (button1, button2) support repeated generation, making it suitable for classroom exploration and learner-driven investigation. Best for students studying sequences and series, as well as for interactive math visualization use in secondary school through early university.