The pattern shows a sequence of triangles constructed using straws. The total number of small triangles formed and the total number of straws used for the first three patterns are shown on the table.
- Find the number of small triangles in Figure 5.
- Find the number of small triangles in Figure 30.
- Find the number of straws in Figure 51.
| Figure |
1 |
2 |
3 |
5 |
30 |
51 |
Number of
small triangles |
1 |
4 |
9 |
(a) ? |
(b) ? |
|
Number of
straws |
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 5
= 5
2 = 25
(b)
Number of small triangles for Figure 30
= 30
2 = 30 x 30
= 900
(c)
Patterns for the number of straws
Figure 1: 3 x (1)
Figure 2: 3 x (1 + 2)
Figure 3: 3 x (1 + 2 + 3)
Formula
Number of straws = 3 x [Figure Number x (Figure number + 1) ÷ 2]
Number of straws in Figure 51
= 3 x (51 x (51+1) ÷ 2)
= 3 x (51 x 52 ÷ 2)
= 3 x (2652 ÷ 2)
= 3 x 1326
= 3978
Answer(s): (a) 25; (b) 900; (c) 3978
