In a linear sequence the terms go up or down by the same amount each time. In 3, 5, 7, 9, … the difference is 2. The nth term rule lets you find any term without listing them all.
The rule starts with the difference times n. Here that is 2n, which gives 2, 4, 6, 8. Each real term is 1 more, so the nth term is 2n + 1. Check with n = 1: 2 × 1 + 1 = 3. You can use the rule to test if a number is in the sequence.
Worked example
Find the nth term of 10, 18, 26, 34, …
- The difference is 8, so start with 8n: 8, 16, 24, 32.
- Each term is 2 more than 8n.
Answer:8n + 2
Key words
- term
- a number in the sequence
- common difference
- the amount added each time
- nth term
- a rule for the term in position n
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