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🔗 Generating Sequences

Build sequences from rules like 'add 3 each time' or formulas like 3n − 2, and tell whether a sequence is arithmetic, geometric, or neither.

lesson

~15 min

to learn

🔢 Math

subject

Ages 6–12

level

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What you’ll learn

Generating SequencesGenerate sequences from term-to-term and position-to-term (nth-term) rules, and classify sequences as arithmetic, geometric, or neither.A sequence is an ordered list following a rule. A term-to-term rule steps from one term to the next — 'start at 2, add 3' gives 2, 5, 8, 11, 14. A position-to-term (nth-term) rule such as 3n − 2 gives any term directly by substituting its position, so the 100th term is 3 × 100 − 2 = 298. Sequences are arithmetic when the difference is constant, geometric when the ratio is constant, and neither otherwise — like the square numbers 1, 4, 9, 16.

Questions this course answers

What is the main advantage of an nth-term (position-to-term) rule?

You can substitute any position n and get that term at once.

Which sequence is geometric (constant ratio)?

3, 6, 12, 24 multiplies by 2 each time — a constant ratio.

Why is the sequence 1, 4, 9, 16 neither arithmetic nor geometric?

These are square numbers; differences (3, 5, 7) and ratios both change.

Grounded in trusted sources

BBC Bitesize — Maths (Key Stage 3)
Khan Academy — Sequences
NRICH (University of Cambridge)
Britannica

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

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