The note
How schools teach it now
Children find the difference between terms and describe the rule in words ('start at 5 and add 4'). Year 6 meets simple formulae; the 'nth term' (4n + 1) is usually Year 7 but appears in some 11+ papers.
5-minute kitchen-table activity
Make a row of squares with matchsticks or cocktail sticks: 1 square needs 4, 2 squares need 7, 3 squares need 10. How many for 10 squares? (It goes up by 3 each time: 31.)
Worked example
What is the 20th term of 5, 9, 13, 17, …?
- It goes up by 4 each time, so the rule starts with 4n.
- For the 1st term, 4 × 1 = 4, but the term is 5, so add 1: the rule is 4n + 1.
- 20th term: 4 × 20 + 1 = 81.
Answer: 81
Common mistakes to watch for
- Using only the difference: 20 × 4 = 80, forgetting the + 1.
- Checking the rule on the first two terms only.
- Missing patterns where the gap changes (1, 2, 4, 7, 11…).
Encouragement
- Try saying
- “What's happening from one number to the next?”
- Rather than
- “You'll just see it if you look.”