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0580/32 Feb/Mar 2025, Question 8: Linear Sequences and Common Difference

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 5 marks

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The question, in short

For the sequence 31, 24, 17, 10, state how terms change, give the following two terms, and find the nth term.

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

Part (a) · 1 mark

Write down the rule linking each term to the next in the sequence.

  1. 124 − 31 = −7, 17 − 24 = −7
  2. 2Subtract 7

Answersubtract 7

Part (b) · 2 marks

Use the rule to find the next two terms after 10.

  1. 1Each term is 7 less than the one before.
  2. 210 − 7 = 3, then 3 − 7 = −4
  3. 3Next two terms: 3, −4

Answer3, −4

Part (c) · 2 marks

Find an expression for the nth term of the sequence.

  1. 1Common difference −7, so −7n
  2. 2First term: 31 = −7 × 1 + 38
  3. 3nth term = 38 − 7n

Answer38 − 7n

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