Pattern Recognition

Algebra 1 · Axiom Academy

Every number sequence hides a rule. Spot whether each step adds the same amount or multiplies by the same amount, and you can predict what comes next. The rule is hiding between the terms A list of numbers looks like just a list — until you ask what takes you from one term to the next. That single repeated move is the whole pattern. Once you can name it, the sequence stops being a memory test and becomes something you can predict. Watch the jump from each term to the next light up, one arc at a time. Every jump is the same size — a constant +4 . A sequence built from one repeated added amount is called arithmetic . Same gap, every single step — that constant difference is the rule. Two kinds of rule: add the same, or multiply the same Generate a pattern, then reveal its rule. Switch between an arithmetic sequence (each step adds the same number) and a geometric one (each step multiplies by the same number). Slide to walk along the terms and watch the differences and ratios light up — only one of them stays constant. Constant difference → arithmetic. Constant ratio → geometric. Test both, every time. Extend the rule to predict what's next Here are five terms with one repeated rule. Drag the empty slot up and down to predict the next term . Land on the value that continues the rule and the slot locks in — that is what pattern recognition buys you: the next term without listing them all. Spot the rule, apply it once more — and the next term is no longer a mystery.

This is the written version of the interactive lesson above. See the full Algebra 1 course.