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4MA1/1FR Jan 2019, Question 9: The nth Term of a Linear Sequence

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1FR (Foundation) · Calculator · 5 marks

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The question, in short

Using the given counter patterns, extend the sequence and determine counter totals and black-counter counts for later pattern numbers.

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

Part (a) · 1 mark

Draw the next pattern in the sequence, continuing the alternating arrangement of white and black counters.

  1. 1Pattern 1 has 2 black counters and 1 white counter
  2. 2Each new pattern has one more black counter and one more white counter
  3. 3So pattern n has n + 1 black counters and n white counters
  4. 4Pattern 4 has 4 + 1 = 5 black counters and 4 white counters
  5. 5Draw Pattern 4 continuing the same arrangement: 5 black and 4 white, 9 counters in all

AnswerPattern 4 drawn correctly: 5 black counters and 4 white counters

Part (b) · 1 mark

Calculate how many counters appear altogether in the sixth pattern.

  1. 1Pattern 1 has 3 counters in total
  2. 2Each new pattern adds 2 more counters
  3. 3Total number of counters in pattern n = 2n + 1
  4. 4Pattern 6: 2 × 6 + 1 = 13

Answer13

Part (c) · 1 mark

Determine how many black counters are present in the fourteenth pattern.

  1. 1Pattern 1 has 2 black counters
  2. 2Each new pattern has one more black counter than the one before
  3. 3Black counters in pattern n = n + 1
  4. 4Pattern 14: 14 + 1 = 15

Answer15

Part (d) · 2 marks

Calculate the combined count of counters in the fiftieth pattern.

  1. 1Counters: 3, 5, 7, … go up by 2 each time.
  2. 2nth term = 2n + 1
  3. 3Pattern 50: 2 × 50 + 1 = 101

Answer101

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