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4MA1/2F Jun 2024, Question 4: Linear Sequences and Common Difference

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2F (Foundation) · Calculator · 4 marks

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The question, in short

A sequence starts 106, 99, 92, 85, 78. Find its next term, justify the method, use the 9th term 50 to get the 12th, and explain why 7 cannot appear.

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

Part (ai) · 1 mark

Give the term that follows 78 in the sequence.

  1. 178 − 7 = 71

Answer71

Part (aii) · 1 mark

State the rule or reasoning used to obtain the term in part (ai).

  1. 199 − 106 = −7
  2. 292 − 99 = −7
  3. 385 − 92 = −7
  4. 478 − 85 = −7
  5. 5The sequence decreases by 7 each time

Answereach term decreases by 7

Part (b) · 1 mark

Using the 9th term 50, calculate the 12th term.

  1. 1Common difference is −7
  2. 29th term = 50
  3. 310th term = 50 − 7 = 43
  4. 411th term = 43 − 7 = 36
  5. 512th term = 36 − 7 = 29

Answer29

Part (c) · 1 mark

Give a reason why 7 is not a term of this sequence.

  1. 1The rule is −7n + 113
  2. 2For n=1: −7(1) + 113 = 106
  3. 3The terms decrease by 7: 106, 99, 92, ..., 15, 8, 1, ...
  4. 4After 8 comes 1, skipping 7
  5. 57 is not in the sequence because it does not fit the pattern of subtracting 7 from the previous term starting from 106

Answerthe sequence goes ..., 15, 8, 1 and so does not include 7

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