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0580/32 May/Jun 2023, Question 9: The nth Term of a Linear Sequence

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 7 marks

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The question, in short

Work with two sequences: continue 2, 8, 14, 20 and find its nth term, then handle sequences from n² + 5 and 7, 10, 15, 22.

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

Part (ai) · 1 mark

State the term that follows 20 in the sequence 2, 8, 14, 20.

  1. 1The terms go up by 6
  2. 220 + 6 = 26

Answer26

Part (aii) · 1 mark

Describe how to get from each term to the next in 2, 8, 14, 20.

  1. 1Each term is 6 more than the one before: add 6

Answeradd 6

Part (aiii) · 2 marks

Find an expression in n for the nth term of 2, 8, 14, 20.

  1. 1Difference 6, so 6n
  2. 2n = 1: 6 × 1 = 6, and 6 − 4 = 2
  3. 3nth term = 6n − 4

Answer6n − 4

Part (bi) · 2 marks

Using nth term n² + 5, write the first three terms.

  1. 1n = 1: 1² + 5 = 6
  2. 2n = 2: 2² + 5 = 9
  3. 3n = 3: 3² + 5 = 14
  4. 46, 9, 14

Answer6, 9, 14

Part (bii) · 1 mark

Find an expression in n for the nth term of 7, 10, 15, 22.

  1. 1Squares: 1, 4, 9, 16
  2. 27, 10, 15, 22 are each 6 more
  3. 3nth term = n² + 6

Answern² + 6

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Also searched as: 0580/32/M/J/23 · 0580_s23_qp_32 · 0580 s23 32 · question 9.
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