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 31.
- Find the number of sticks in Figure 51.
Figure |
1 |
2 |
3 |
4 |
31 |
51 |
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 31
= 31
2 = 31 x 31
= 961
(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 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) 16; (b) 961; (c) 3978