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Year 7 · Patterns & Algebra

nth term of a linear sequence

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

Find the nth term of the sequence 4, 1, -2, -5, …
The sequence goes up by -3 each time, so the rule starts with -3n. The term before the first would be 7, so the nth term is -3n+7.
Answer: -3n+7

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

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