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4MA1/2F Jan 2022, Question 11: Pattern Sequences and Special Sequences

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

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The question, in short

Using a growing counter pattern where patterns 1 to 3 use 3, 6 and 9 counters, draw the next pattern, fill a table, find the count for pattern 10, and decide if 70 counters suffice for pattern 25.

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

Part (a) · 1 mark

Draw the fourth pattern in the sequence, continuing the counter arrangement shown for patterns 1 to 3.

  1. 1Pattern number 4 has 4 rows of 3 counters each, arranged in a vertical line with 3 counters per row

AnswerPattern number 3 continued in the same way with 3 more counters, giving 12 counters

Part (b) · 1 mark

Fill in the missing counter totals for patterns 4 and 5 in the given table.

  1. 1Pattern number 1: 3 counters
  2. 2Pattern number 2: 6 counters
  3. 3Pattern number 3: 9 counters
  4. 4Each pattern increases by 3 counters
  5. 5Pattern number 4: 9 + 3 = 12
  6. 6Pattern number 5: 12 + 3 = 15

Answer12, 15

Part (c) · 1 mark

Calculate how many counters pattern number 10 contains.

  1. 1Each pattern number n has 3n counters
  2. 2Pattern number 10: 3 × 10 = 30

Answer30

Part (d) · 1 mark

Decide whether Sven's 70 counters are enough for pattern 25, tick Yes or No, and justify the choice.

  1. 1Pattern number n has 3n counters
  2. 2Sven has 70 counters, which is not enough for 3 × 25
  3. 3No, Pattern number 25 needs 3 × 25 = 75 counters

AnswerNo, Pattern number 25 needs 3 × 25 = 75 counters

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