Pattern Detective

Algebra 2 · Axiom Academy

Every sequence hides a rule. Find it, and you can predict not just the next term, but any term a_n at all. A list of numbers with a secret rule A sequence is just an ordered list of numbers — but the interesting ones are built by a rule. Spot the rule and the list stops being a mystery: you can say exactly what comes next, and jump to any position you like. Watch one build itself, then crack a few yourself. Watch the sequence assemble one term at a time. Each new term is the one before it plus the same constant jump — and once that rule is clear, it tells you the unknown next term before you even reach it. The jump is the same every step — that constant rule is what lets you predict what comes next. Here's a sequence with its next term hidden. Read the jump from one term to the next, work out the rule, and pick what comes next. Each new pattern is built by a different kind of rule. Every sequence in this unit is built one of three ways: add a constant (arithmetic), multiply by a constant (geometric), or something else entirely (nonlinear). Read each one and name its rule. What kind of rule generates this sequence? From spotting rules to formulas You just did the one move this whole unit is built on: read a list of numbers, find the rule that generates it, and use that rule to predict what comes next.

This is the written version of the interactive lesson above. See the full Algebra 2 course.