The figures shows a sequence of patterns of an arrangement of dots. "1st row" indicates the number of dots in the first row and the "Total" indicates the number of dots in each pattern.
- Find the number of dots in Figure 12.
- Find the number of dots in Figure 54.
- If the first row of a figure is made up of 87 dots, find the number of dots that make up the figure.
(a)
Pattern for number of dots
Figure 1: 1 x 3 + 4 = 7
Figure 2: 2 x 3 + 4 = 10
Figure 3: 3 x 3 + 4 = 13
Number of dots = Figure number x 3 + 4
Number of dots in Figure 12
= 12 x 3 + 4
= 40
(b)
Number of dots in Figure 54
= 54 x 3 + 4
= 166
(c)
Pattern for number of dots in first row
Figure 1: 1 + 2 = 3
Figure 2: 2 + 2 = 4
Figure 3: 3 + 2 = 5
Figure Number = Number of dots in first row - 2
Number of figure with 87 dots in first row
= 87 - 2
= 85
Number of dots in Figure 85
= 85 x 3 + 4
= 259
Answer(s): (a) 40; (b) 166; (c) 259