Study the series of figures carefully.
- Complete the table.
- Find the number of sticks needed in Pattern Number 31.
- Find the number of dots needed when 743 sticks are used.
Pattern Number |
Number of sticks |
Number of dots |
1 |
3 |
3 |
2 |
8 |
5 |
3 |
13 |
7 |
... |
... |
... |
17 |
? |
35 |
18 |
71 |
? |
(a)
Pattern for the number of sticks
Pattern 1: 1 x 4 - 1 = 3 sticks
Pattern 2: 2 x 4 - 1 = 7 sticks
Pattern 3: 3 x 4 - 1 = 11 sticks
Formula:
Number of sticks needed = Pattern number x 4 - 1
Number of sticks needed for Pattern 17
= 17 x 4 - 1
= 67
Pattern for the number of dots
Pattern 1: 1 x 2 + 1 = 3 dots
Pattern 2: 2 x 2 + 1 = 5 dots
Pattern 3: 3 x 2 + 1 = 7 dots
Formula:
Number of dots = (Pattern Number x 2) + 1
Number of dots needed for Pattern 18
= 18 x 2 + 1
= 37
(b)
Number of sticks needed in Pattern 31
= 31 x 4 - 1
= 123
(c)
Pattern Number x 4 - 1 = 743
Pattern Number x 4 = 743 + 1 = 744
Pattern number = 744 ÷ 4 = 186
Number of dots needed in Pattern 186
= 186 x 2 + 1
= 373
Answer(s): (a) 37, 67; (b) 123; (c) 373