The pattern shows a sequence of triangles constructed using rods. The total number of small triangles formed and the total number of rods used for the first three patterns are shown on the table.
- Find the number of small triangles in Figure 8.
- Find the number of small triangles in Figure 33.
- Find the number of rods in Figure 46.
| Figure |
1 |
2 |
3 |
8 |
33 |
46 |
Number of
small triangles |
1 |
4 |
9 |
(a) ? |
(b) ? |
|
Number of
rods |
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 8
= 8
2 = 64
(b)
Number of small triangles for Figure 33
= 33
2 = 33 x 33
= 1089
(c)
Patterns for the number of rods
Figure 1: 3 x (1)
Figure 2: 3 x (1 + 2)
Figure 3: 3 x (1 + 2 + 3)
Formula
Number of rods = 3 x [Figure Number x (Figure number + 1) ÷ 2]
Number of rods in Figure 46
= 3 x (46 x (46+1) ÷ 2)
= 3 x (46 x 47 ÷ 2)
= 3 x (2162 ÷ 2)
= 3 x 1081
= 3243
Answer(s): (a) 64; (b) 1089; (c) 3243
