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 9.
- Find the number of dots in Figure 69.
- If the first row of a figure is made up of 83 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 9
= 9 x 3 + 4
= 31
(b)
Number of dots in Figure 69
= 69 x 3 + 4
= 211
(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 83 dots in first row
= 83 - 2
= 81
Number of dots in Figure 81
= 81 x 3 + 4
= 247
Answer(s): (a) 31; (b) 211; (c) 247