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0580/12 Oct/Nov 2021, Question 17: The nth Term of a Linear Sequence

Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Calculator · 6 marks

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The question, in short

A sequence begins 3, 10, 17, 24. Find the next term, the term to term rule, the nth term, and the 40th term.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 1 mark

Write down the term that follows 24 in the sequence.

  1. 124 + 7 = 31

Answer31

Part (b) · 1 mark

State the rule that takes each term to the next.

  1. 1Each term is 7 more than the one before: + 7

Answer+ 7

Part (c) · 2 marks

Find an expression for the nth term of the sequence.

  1. 1Difference 7, so nth term = 7n + b
  2. 27 × 1 + b = 3, so b = −4
  3. 3nth term = 7n − 4

Answer7n − 4

Part (d) · 2 marks

Use your nth term to work out the 40th term.

  1. 140th term = 7 × 40 − 4
  2. 2= 280 − 4 = 276

Answer276

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