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0580/11 Oct/Nov 2021, Question 12: The nth Term of a Linear Sequence

Cambridge IGCSE Mathematics 0580 · Paper 11 (Core) · Calculator · 4 marks

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The question, in short

Three number sequences are given; students must continue the first, state how consecutive terms change in the second, and derive an expression for the nth term of the third.

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Part (a) · 1 mark

Work out the value that comes after 25 in the sequence 7, 13, 19, 25.

  1. 1The terms go up by 6
  2. 2Next term = 25 + 6 = 31

Answer31

Part (b) · 1 mark

Describe the rule linking each term to the one before it in 30, 26, 22, 18.

  1. 130 − 26 = 4, 26 − 22 = 4, 22 − 18 = 4
  2. 2Rule: subtract 4

AnswerSubtract 4

Part (c) · 2 marks

Obtain an expression in n for the sequence −1, 1, 3, 5.

  1. 1Difference = 2, so nth term = 2n + c
  2. 21st term: 2 × 1 + c = −1, so c = −3
  3. 3nth term = 2n − 3

Answer2n − 3

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Also searched as: 0580/11/O/N/21 · 0580_w21_qp_11 · 0580 w21 11 · question 12.
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