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0580/21 Oct/Nov 2024, Question 13: Pattern Sequences and Special Sequences

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 5 marks

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The question, in short

Use the given nth term rule to get a term of a sequence, and work out nth term formulas for sequences A and B from their first five terms.

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Part (a) · 1 mark

Substitute n = 2 into 3n² − 1 to work out the second term.

  1. 13 × 2² − 1 = 12 − 1 = 11

Answer11

Part (b) · 4 marks

For sequences A and B, use the listed first five terms to fill in the nth term column of the table.

  1. 1A: the terms go up by 4, so 4n + c; 4 × 1 + c = −6 → c = −10
  2. 2Sequence A: 4n − 10
  3. 3B: differences 14, 38, 74, 122; then 24, 36, 48; then 12 (constant), so cubic with n³ coefficient 12 ÷ 6 = 2
  4. 4B − 2n³: 3 − 2 = 1, 17 − 16 = 1, 55 − 54 = 1, so add 1
  5. 5Sequence B: 2n³ + 1

AnswerSequence A: 4n − 10, Sequence B: 2n³ + 1

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Also searched as: 0580/21/O/N/24 · 0580_w24_qp_21 · 0580 w24 21 · question 13.
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