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4024/12 May/Jun 2022, Question 9: Pattern Sequences and Special Sequences

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 6 marks

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The question, in short

Using a counter pattern sequence shown in a diagram, complete a table, derive a formula for the nth pattern, and use 100 counters to find a second pattern number.

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

Part (a) · 1 mark

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

  1. 1Add 3 counters each time
  2. 211 + 3 = 14, 14 + 3 = 17

Answer14, 17

Part (b) · 2 marks

Write an expression involving n that gives the counter count for pattern n.

  1. 1Difference is 3, so 3n + …
  2. 2n = 1: 3 × 1 + 2 = 5
  3. 33n + 2

Answer3n + 2

Part (c) · 3 marks

After building pattern 20 from 100 counters, determine k for the pattern made with what remains.

  1. 1Pattern 20 uses 3 × 20 + 2 = 62 counters
  2. 2100 − 62 = 38 counters left
  3. 33k + 2 = 38, so 3k = 36
  4. 4k = 12

Answer12

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