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 4.
- Find the number of small triangles in Figure 25.
- Find the number of sticks in Figure 76.
Figure |
1 |
2 |
3 |
4 |
25 |
76 |
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 4
= 4
2 = 16
(b)
Number of small triangles for Figure 25
= 25
2 = 25 x 25
= 625
(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 76
= 3 x (76 x (76+1) ÷ 2)
= 3 x (76 x 77 ÷ 2)
= 3 x (5852 ÷ 2)
= 3 x 2926
= 8778
Answer(s): (a) 16; (b) 625; (c) 8778