The nth term, and geometric sequences
Build a table from a matchstick pattern, find its nth term and use it to count figure 20 without drawing it. Then meet sequences that multiply each time.
- UK: Year 8
- France: grade 11
- Iran: grade 7
- Syria: grade 11
- Ukraine: grade 9
- Russia: grade 9
Guide
This studio follows Year 8 (KS3 "generate terms of a sequence from a term-to-term or a position-to-term rule", "recognise geometric sequences"). In the matchstick squares, figure 1 has four sticks and each new square adds 3. The nth term is 3n + 1, where n is the figure number.
The rule "add 3 each time" says how to get from one term (of a sequence) to the next; the nth term gives any term straight from its position. For figure 20 you need not add 19 times: 3 × 20 + 1 = 61.
In a geometric sequence each term is the one before times a fixed number (×2, ×12), not plus. In 2, 4, 8, 16, … the nth term is 2n, not 2n.
Common mistakes: n + 3 for 4, 7, 10, … (the jump ignored); giving the term-to-term rule as the nth term; continuing a geometric sequence by adding; mixing up 2n and 2n.