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4024/12 Oct/Nov 2023, Question 15: Linear Sequences and Common Difference

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Given a linear sequence with second term 28 and fifth term 16, work out the missing first, third and fourth terms, then find the nth term formula for the sequence 3, 9, 19, 33, 51.

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Part (a) · 2 marks

Using the 2nd term 28 and 5th term 16 of a linear sequence, determine the 1st, 3rd and 4th terms.

  1. 1From 2nd term to 5th term is 3 steps: d = (16 − 28) ÷ 3 = −4
  2. 2First term = 28 + 4 = 32
  3. 3Third term = 28 − 4 = 24, fourth term = 24 − 4 = 20
  4. 4First term = 32, third term = 24, fourth term = 20

AnswerFirst term = 32, Third term = 24, Fourth term = 20

Part (b) · 2 marks

For the sequence 3, 9, 19, 33, 51, derive an expression giving the nth term.

  1. 1First differences: 6, 10, 14, 18
  2. 2Second differences: 4, 4, 4 so the nth term starts 2n²
  3. 32n²: 2, 8, 18, 32, 50; sequence − 2n² = 1 each time
  4. 4nth term = 2n² + 1

Answer2n² + 1

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