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Number Patterns

Number Patterns

TGM Original Questions

A sequence of patterns formed by dots and lines is shown below.

  1. Draw Pattern \(4\).
  2. Complete the following table:
    List item image
  3. Based on your answers in (ii), find
    1. the number of dots and lines, respectively, to make pattern \(50\).
    2. the pattern number that uses a total of \(2024\) dots. Hence find the number of lines in this pattern.
  4. Find a formula that represents the relationship between the number of dots, \(D\), the number of lines, \(L\), and the pattern number, \(n\), in the sequence shown above.

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Answer:(i) Pattern 4 has four connected octagons (ii) Pattern 4: \(D=26\), \(L=29\) Pattern 5: \(D=32\), \(L=36\) Pattern \(n\): \(D=6n+2\), \(L=7n+1\) (iii)(a) \(302\) dots and \(351\) lines (iii)(b) Pattern \(337\) and \(2360\) lines (iv) \(D=L-n+1\)

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