Study the series of figures carefully.
- Complete the table.
- Find the number of sticks needed in Pattern Number 27.
- Find the number of dots needed when 539 sticks are used.
Pattern Number |
Number of sticks |
Number of dots |
1 |
3 |
3 |
2 |
8 |
5 |
3 |
13 |
7 |
... |
... |
... |
13 |
? |
27 |
14 |
55 |
? |
(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 13
= 13 x 4 - 1
= 51
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 14
= 14 x 2 + 1
= 29
(b)
Number of sticks needed in Pattern 27
= 27 x 4 - 1
= 107
(c)
Pattern Number x 4 - 1 = 539
Pattern Number x 4 = 539 + 1 = 540
Pattern number = 540 ÷ 4 = 135
Number of dots needed in Pattern 135
= 135 x 2 + 1
= 271
Answer(s): (a) 29, 51; (b) 107; (c) 271