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4024/11 Oct/Nov 2022, Question 13: Pattern Sequences and Special Sequences

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

For a sequence given by 3n² − 1, work out its first three terms, and for the sequence 1, 3, 9, 27, 81 find a formula for the nth term in terms of n.

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Part (a) · 2 marks

Using the rule 3n² − 1, calculate the values of the first three terms of the sequence.

  1. 1n = 1: 3 × 1 − 1 = 2
  2. 2n = 2: 3 × 4 − 1 = 11
  3. 3n = 3: 3 × 9 − 1 = 26

Answer2, 11, 26

Part (b) · 2 marks

From the terms 1, 3, 9, 27, 81, determine an expression involving n that generates the nth term.

  1. 1Each term × 3, first term 1 = 3⁰
  2. 2nth term = 3ⁿ⁻¹

Answer3ⁿ⁻¹

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