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 19.
- Find the number of dots in Figure 91.
- If the first row of a figure is made up of 63 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 19
= 19 x 3 + 4
= 61
(b)
Number of dots in Figure 91
= 91 x 3 + 4
= 277
(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 63 dots in first row
= 63 - 2
= 61
Number of dots in Figure 61
= 61 x 3 + 4
= 187
Answer(s): (a) 61; (b) 277; (c) 187