Study the series of figures carefully.
- Complete the table.
- Find the number of sticks needed in Pattern Number 26.
- Find the number of dots needed when 335 sticks are used.
Pattern Number |
Number of sticks |
Number of dots |
1 |
3 |
3 |
2 |
8 |
5 |
3 |
13 |
7 |
... |
... |
... |
8 |
? |
17 |
9 |
35 |
? |
(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 8
= 8 x 4 - 1
= 31
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 9
= 9 x 2 + 1
= 19
(b)
Number of sticks needed in Pattern 26
= 26 x 4 - 1
= 103
(c)
Pattern Number x 4 - 1 = 335
Pattern Number x 4 = 335 + 1 = 336
Pattern number = 336 ÷ 4 = 84
Number of dots needed in Pattern 84
= 84 x 2 + 1
= 169
Answer(s): (a) 19, 31; (b) 103; (c) 169