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.

1. Find the number of dots in Figure 15.
2. Find the number of dots in Figure 52.
3. If the first row of a figure is made up of 48 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 52
= 52 x 3 + 4
= 160

(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 48 dots in first row
= 48 - 2
= 46

Number of dots in Figure 46
= 46 x 3 + 4
= 142

Answer(s): (a) 49; (b) 160; (c) 142