Study the series of figures carefully.
- Complete the table.
- Find the number of sticks needed in Pattern Number 23.
- Find the number of dots needed when 447 sticks are used.
Pattern Number |
Number of sticks |
Number of dots |
1 |
3 |
3 |
2 |
8 |
5 |
3 |
13 |
7 |
... |
... |
... |
12 |
? |
25 |
13 |
51 |
? |
(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 12
= 12 x 4 - 1
= 47
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 13
= 13 x 2 + 1
= 27
(b)
Number of sticks needed in Pattern 23
= 23 x 4 - 1
= 91
(c)
Pattern Number x 4 - 1 = 447
Pattern Number x 4 = 447 + 1 = 448
Pattern number = 448 ÷ 4 = 112
Number of dots needed in Pattern 112
= 112 x 2 + 1
= 225
Answer(s): (a) 27, 47; (b) 91; (c) 225