🔎 Finding Rules in Number Patterns

What you’ll learn

1. The Step-by-Step RuleFind the term-to-term (step-by-step) rule of a sequence and use it to continue the pattern.A term-to-term rule tells you how each number becomes the next. In 2, 5, 8, 11 the jump is always +3, so the next term is 14. Some patterns add, some subtract, some multiply — find the constant change and apply it to keep the sequence going.
2. The Position RuleFind the position (nth-term) rule linking a term's position to its value.The position rule connects where a term sits to its value. For 3, 6, 9, 12, each value equals its position × 3, so position 5 gives 15 and position 8 gives 24. Unlike the step-by-step rule, the position rule reaches any term in a single multiply.
3. Predict Far AheadUse the position rule to predict far-off terms efficiently.The power of the position rule shows up with distant terms. Reaching the 10th term of 3, 6, 9... by adding takes nine steps, but the rule does it in one: 10 × 3 = 30. Recognizing a sequence's rule — add, subtract, double — lets you predict any term you like.

Questions this course answers

Grounded in trusted sources

• Khan Academy
• NRICH — University of Cambridge
• NCTM — teaching standards
• Britannica Kids

Every Wunder lesson is built from real, reputable sources — never invented.

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