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0580/43 May/Jun 2021, Question 11: The nth Term of a Linear Sequence

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 9 marks

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The question, in short

Sequence questions: for 11, 7, 3, −1 find the next term, the term-to-term rule and the nth term; for 2n/(n + 1) compare the 5th and 6th terms and test whether 3/4 occurs.

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Part (ai) · 1 mark

Write down the term that follows −1 in the sequence 11, 7, 3, −1.

  1. 1Each term is 4 less: −1 − 4 = −5

Answer−5

Part (aii) · 1 mark

State the rule that takes each term to the next in 11, 7, 3, −1.

  1. 1Subtract 4

AnswerSubtract 4

Part (aiii) · 2 marks

Find an expression in n for the nth term of 11, 7, 3, −1.

  1. 1Difference is −4, so nth term = −4n + k
  2. 2n = 1: −4 + k = 11, so k = 15
  3. 3nth term = 15 − 4n

Answer15 − 4n

Part (bi) · 2 marks

For the sequence with nth term 2n/(n + 1), find the 5th and 6th terms and their difference as a fraction.

  1. 15th term = (2 × 5)/(5 + 1) = 10/6 = 5/3
  2. 26th term = (2 × 6)/(6 + 1) = 12/7
  3. 3Difference = 12/7 − 5/3 = 36/21 − 35/21 = 1/21

Answer1/21

Part (bii) · 3 marks

Decide whether 3/4 is a term of the sequence with nth term 2n/(n + 1), showing your reasoning.

  1. 13/4 = 2n/(n + 1)
  2. 23(n + 1) = 8n, so 3n + 3 = 8n
  3. 35n = 3, so n = 3/5
  4. 4No: n = 3/5 is not an integer, so 3/4 is not a term

AnswerNo: 3/4 = 2n/(n + 1) gives n = 3/5, which is not an integer (or: 2n ≥ n + 1 so every term is at least 1, but 3/4 is less than 1)

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Also searched as: 0580/43/M/J/21 · 0580_s21_qp_43 · 0580 s21 43 · question 11.
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