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 11.
- Find the number of dots in Figure 51.
- If the first row of a figure is made up of 43 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 11
= 11 x 3 + 4
= 37
(b)
Number of dots in Figure 51
= 51 x 3 + 4
= 157
(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 43 dots in first row
= 43 - 2
= 41
Number of dots in Figure 41
= 41 x 3 + 4
= 127
Answer(s): (a) 37; (b) 157; (c) 127