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 15.
- Find the number of dots in Figure 37.
- If the first row of a figure is made up of 65 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 15
= 15 x 3 + 4
= 49
(b)
Number of dots in Figure 37
= 37 x 3 + 4
= 115
(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 65 dots in first row
= 65 - 2
= 63
Number of dots in Figure 63
= 63 x 3 + 4
= 193
Answer(s): (a) 49; (b) 115; (c) 193