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 7.
- Find the number of dots in Figure 53.
- If the first row of a figure is made up of 80 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 7
= 7 x 3 + 4
= 25
(b)
Number of dots in Figure 53
= 53 x 3 + 4
= 163
(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 80 dots in first row
= 80 - 2
= 78
Number of dots in Figure 78
= 78 x 3 + 4
= 238
Answer(s): (a) 25; (b) 163; (c) 238