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4024/11 Oct/Nov 2020, Question 18: Pattern Sequences and Special Sequences

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Rows of numbers grow: each row has one more entry and entries increase by two. Use the given rows to complete Row 5 and find expressions in n for Row n.

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

Part (a) · 1 mark

Write out the numbers in Row 5, following the pattern of one extra number and values two larger.

  1. 1Row 5 has 6 numbers, each 9 + 2 = 11
  2. 211 11 11 11 11 11

Answer11 11 11 11 11 11

Part (b) · 1 mark

Give an expression in n for the value repeated in each position of Row n.

  1. 1Numbers 3, 5, 7, 9: go up by 2
  2. 2Each number = 2n + 1

Answer2n + 1

Part (c) · 1 mark

Give an expression in n for how many numbers Row n contains.

  1. 1Counts 2, 3, 4, 5
  2. 2Number of numbers = n + 1

Answern + 1

Part (d) · 1 mark

Give an expression in n for the total of all numbers in Row n.

  1. 1Sum = each number × how many
  2. 2= (2n + 1)(n + 1) = 2n² + 3n + 1

Answer(2n + 1)(n + 1) or 2n² + 3n + 1

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Also searched as: 4024/11/O/N/20 · 4024_w20_qp_11 · 4024 w20 11 · question 18.
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