Interactive Questioning & Experimentation: Geometry–Algebra Links for Sequences

This GeoGebra lesson uses button-driven interactions to guide students through a questioning–experimenting cycle: propose a conjecture from what they see, test it by changing conditions, and observe how key “special points” respond. It connects number-theory ideas (LCM/GCD structure), pattern recognition in sequences and series, and planar geometric reasoning about point configurations under constraints. Construction is centered on interactive controls (button1–button6) for switching scenarios or parameters, multiple text objects (text1–text6) for displaying questions and results, a state variable to manage the current stage, and points A–F to visualize the evolving special positions on the plane. Ideal for middle school advanced through high school inquiry-based learning, practice with mathematical modeling, and interactive classroom activities focused on discovery.