Geometric Sequences Filling a Gap via Construction

This example visualizes how a geometric sequence (equal-ratio recursion) can be used to “fill a gap” in a geometric figure: successive points and segments are generated so that their lengths follow a common ratio, producing a clear gap-filling pattern. Key math concepts include geometric sequences, first term and common ratio, ratio-based recursion, and the geometric interpretation behind geometric-series-like step scaling. Construction-wise, the GeoGebra setup uses RandomElement and Random for randomized choices, If for conditional logic, Textfield/InputBox1 for interactive parameter entry and on-screen labels, and AreEqual to control branching when conditions match. It creates lists such as rlist, a1list, a2list, a3list and parameter containers like a1, a2, a3, rR, rA, qlist; it also prepares step markers t1–t7 and annotation texts (text1–text8). Point objects P1–P7 are then used to place the geometric elements, while button1/button2 and other controls (e.g., ha, stans, nN, AnsW) manage iteration and the interactive visualization. Suitable for middle/high school learners and early university students for teaching sequence reasoning and geometric construction with ratio-driven patterns.