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0580/13 Oct/Nov 2021, Question 14: The nth Term of a Linear Sequence

Cambridge IGCSE Mathematics 0580 · Paper 13 (Core) · Calculator · 4 marks

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The question, in short

Two sequences are given by their first four terms: 17, 23, 29, 35 and 3, −1, −5, −9. Find the next term of each and the nth term of the second.

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Part (a) · 1 mark

Find the term after 35 in the sequence 17, 23, 29, 35.

  1. 1The terms go up by 6: 35 + 6 = 41

Answer41

Part (bi) · 1 mark

Find the term after −9 in the sequence 3, −1, −5, −9.

  1. 1The terms go down by 4: −9 − 4 = −13

Answer−13

Part (bii) · 2 marks

Find an expression for the nth term of the sequence 3, −1, −5, −9.

  1. 1Difference −4, so nth term = −4n + k
  2. 21st term: −4 × 1 + k = 3, so k = 7
  3. 3nth term = −4n + 7

Answer−4n + 7

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