The first four figures of a pattern as shown.
The table shows the number of dots and the number of non-overlapping triangles for each figure.
- Find the values of (i) and (ii). Give your answers in the following format. (Eg 1, 2)
- What is the number of dots in Figure 15?
- In which Figure number will there be 111 dots?
(a)
(i)
Number of dots:
Figure 1: 6 = 1 + 1 x 5
Figure 2: 11 = 1 + 2 x 5
Figure 3: 16 = 1 + 3 x 5
Figure 4: 21 = 1 + 4 x 5
Formula:
Number of dots = 1 + Figure Number x 5
Number of dots in Figure 5
= 1 + 5 x 5
= 1 + 25
= 26
(ii)
Number of non-overlapping triangles:
Figure 1: 5 =
5 x 1Figure 2: 10 =
5 x 2Figure 3: 20 =
5 x
4 (Notice that '3' is skipped)
Figure 4: 25 =
5 x 5Figure 5: 35 =
5 x
7 (Notice that 6 is skipped)
Figure 6: 40 =
5 x 8 Number of non-overlapping triangles for each figure is a multiple of 5.
So, the number '
5' is one of the factors.
The pattern of the other factor in each equation is as follows:
1, 2, (skip 3) 4, 5, (skip 6) 7, 8, (skip 9) 10, 11, (skip 12) 13, 14, (skip 15) 16, 17 Number of overlapping triangles in Figure 5
= 7 x 5
= 35
(b)
Number of dots in Figure 15
= 1 + 15 x 5
= 1 + 75
= 76
(c)
1 + Figure Number x 5 = 111
Figure Number x 5 = 111 - 1
Figure Number x 5 = 110
Figure Number = 110 ÷ 5
Figure Number = 22
Answer(s): (a) 26, 35; (b) 76; (c) 22