The pattern shows a sequence of triangles constructed using sticks. The total number of small triangles formed and the total number of sticks used for the first three patterns are shown on the table.
- Find the number of small triangles in Figure 7.
- Find the number of small triangles in Figure 27.
- Find the number of sticks in Figure 68.
Figure |
1 |
2 |
3 |
7 |
27 |
68 |
Number of small triangles |
1 |
4 |
9 |
(a) ? |
(b) ? |
|
Number of sticks |
3 |
9 |
18 |
... |
|
(c) ? |
(a)
Pattern for the number of small triangles
Figure 1: 1
2 = 1
Figure 2: 2
2 = 4
Figure 3: 3
2 = 9
Formula
Number of small triangles = Figure number
2 Number of small triangles for Figure 7
= 7
2 = 49
(b)
Number of small triangles for Figure 27
= 27
2 = 27 x 27
= 729
(c)
Patterns for the number of sticks
Figure 1: 3 x (1)
Figure 2: 3 x (1 + 2)
Figure 3: 3 x (1 + 2 + 3)
Formula
Number of sticks = 3 x [Figure Number x (Figure number + 1) ÷ 2]
Number of sticks in Figure 68
= 3 x (68 x (68+1) ÷ 2)
= 3 x (68 x 69 ÷ 2)
= 3 x (4692 ÷ 2)
= 3 x 2346
= 7038
Answer(s): (a) 49; (b) 729; (c) 7038