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4024/11 Oct/Nov 2021, Question 20: 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

Given the first five terms 4, 8, 16, 32, 64 of a sequence, find the next term and derive nth-term expressions for two related sequences.

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

Part (a) · 1 mark

Find the next number after 4, 8, 16, 32, 64 in the sequence.

  1. 1Each term doubles: 64 × 2 = 128

Answer128

Part (bi) · 1 mark

Using 2ⁿ⁺¹ for the original sequence, write an nth-term expression for 1, 5, 13, 29, 61.

  1. 11, 5, 13, 29, 61 are each 3 less than 4, 8, 16, 32, 64
  2. 2nth term = 2ⁿ⁺¹ − 3

Answer2ⁿ⁺¹ − 3

Part (bii) · 2 marks

Using 2ⁿ⁺¹ for the original sequence, write an nth-term expression for 10, 19, 32, 53, 90.

  1. 1Subtract 2ⁿ⁺¹: 10 − 4, 19 − 8, 32 − 16, 53 − 32, 90 − 64 = 6, 11, 16, 21, 26
  2. 26, 11, 16, 21, 26 has nth term 5n + 1
  3. 3nth term = 2ⁿ⁺¹ + 5n + 1

Answer2ⁿ⁺¹ + 5n + 1

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Also searched as: 4024/11/O/N/21 · 4024_w21_qp_11 · 4024 w21 11 · question 20.
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