The diagram of the sequence of circular and square tiles gives;
a) 49
b) 84
c) Will always be odd
<h3>Which method can be used to find the order of the sequence in the pattern?</h3>
Pattern 1
Number of square tiles = 1
Number of circular tiles = 8
Total number of tiles = 9
Pattern 2
Number of square tiles = 4
Number of circular tiles = 12
Total number of tiles = 16
Pattern 3
Number of square tiles = 9
Number of circular tiles = 16
Total number of tiles = 25
- The number of square tiles required to make pattern <em>n </em>= n²
From the diagram, the number of circular tiles on the left or right side of the square tiles are 2 more than the number of square tiles, while the number of circular tiles on the top or bottom are the same as the number of square tiles, therefore;
- Number of circular tiles = 2•(n + 2) + 2•n
a) The number of square tiles required to make pattern number 7 = 7² = 49
b) The number of circular tiles needed to make pattern number 20 = 2 × 20 + 2 × (20 + 2) = 84
c) The total number of circular tiles is always even while the number of square tiles has the same characteristics (even or odd) as the pattern number
- Even + Odd = Odd
- Even + Even = Even
When the pattern number is odd, the total number of tiles will always be odd. The correct option is therefore;
B. Will always be odd
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