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Sequences and the nth term
Years 4 to 10
A sequence follows a rule. The nth term is a formula that gives any term from its position.
For learners
A sequence is a list of numbers that follows a rule. 4, 7, 10, 13 goes up by 3 each time.
The nth term is a rule that tells you any number in the list. Here the steps are 3, so the rule starts with 3n.
Check the first term: 3 × 1 = 3, but we need 4. So add 1. The rule is 3n + 1.
A worked example
Find the nth term of 5, 9, 13, 17.
- The steps are 4, so it starts with 4n.
- 4 × 1 = 4, and the first term is 5, so add 1.
- The nth term is 4n + 1.
For grown-ups
The number in front of n is the step size. Then check the first term and adjust. For quadratic sequences the first differences change, and the second difference is twice the number in front of n².
Common mistakes
- Using the first term as the number in front of n.
- Forgetting to add or subtract the correction.
- Mixing up the term number n with the term's value.
Why it matters
Patterns in numbers show up in saving money, growing populations and computer programs.
Topics in quarter that use this
- Number sequences
- The nth term
- Quadratic sequences
- Arithmetic sequences and series