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Year 6 · Patterns & Algebra

Number sequences: find the term

A linear sequence goes up or down by the same amount. Its nth term is a rule like 3n + 2.

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How to do it

  1. Find the common difference: that is the number in front of n.
  2. Work out what comes before the first term: that is the constant.
  3. For a far term, substitute n into the rule.

Worked example

What is the 20th term of 12, 15, 18, 21, …
nth term = 3n+9. Put n = 20: 3 × 20 + 9 = 69.
Answer: 69

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Check the rule with n = 1: 3 × 1 + 2 = 5 ✓

Practise Number sequences: find the term properly

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