Writing Recursive Formulas for Mathematical Sequences

Miacademy & MiaPrep Learning Channel

This video provides a comprehensive tutorial on how to write recursive formulas for mathematical sequences. Building on previous knowledge of using formulas, the lesson transitions students into creating their own formulas based on observed patterns. The instructor, Justin, guides viewers through a systematic three-step process: identifying the pattern, writing the recursive relationship using proper notation (like a_n and a_n-1), and establishing the necessary starting values to define the sequence completely. The content covers three distinct types of sequences: arithmetic sequences (where a constant is added), geometric sequences (where the previous term is multiplied by a constant), and more complex patterns where a term depends on two previous terms (similar to the Fibonacci sequence). The video specifically addresses the notation required when referencing terms further back, such as a_n-2, and emphasizes the rule that the number of starting values must match the number of previous terms used in the formula. This resource is highly valuable for Algebra students moving from concrete arithmetic to abstract algebraic notation. By breaking down the "hardest part"—identifying the pattern—and offering shortcuts for standard arithmetic and geometric sequences, the video empowers students to formalize their mathematical thinking. The inclusion of non-standard examples, like a sequence formed by subtracting the previous term from the one before it, challenges students to think critically about order of operations and dependency in recursive logic.