Number Patterns

A number pattern is a sequence built by a fixed rule, and each entry is a term. Spotting the rule lets you extend the sequence or fill a gap, which is the early root of algebraic thinking. The common families: arithmetic patterns add a constant (5, 10, 15, 20 adds 5); geometric patterns multiply by a constant (2, 4, 8, 16 doubles); square numbers come from squaring positions (1, 4, 9, 16, 25 = 1^2, 2^2, 3^2, 4^2, 5^2); triangular numbers add the next counting number each time (1, 3, 6, 10, 15); a Fibonacci-like rule adds the two previous terms (1, 1, 2, 3, 5, 8); and alternating patterns apply two operations in turn. Consecutive numbers sit next to each other with a fixed gap: consecutive natural numbers differ by 1, consecutive even or odd numbers differ by 2, consecutive multiples of k differ by k. Worth remembering: the sum of two consecutive natural numbers is always odd, and the sum of three consecutive natural numbers is always divisible by 3 (since (n-1) + n + (n+1) = 3n). To find a missing term, test for a common difference, then a multiply rule, then position-based or alternating patterns. The classic error is to fix on the first one or two gaps before checking the whole sequence.

✅ Solved examples

✏️ Practice — try these, take hints as needed

📝 Topic test — 8 questions

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