Read the pattern and complete the table.

1. Find the number of circles in Figure 20.
2. Find the figure number that would require a total number of 157 rectangles and circles altogether.

(a)
Pattern for the number of rectangles
Figure 1: 1 rectangle
Figure 2: 2 rectangles
Figure 3: 3 rectangles

Formula:
Number of rectangles = Figure number

Pattern for the number of circles
Figure 1: 1 + 1 x 3 = 4 circles
Figure 2 : 1 + 2 x 3 = 7 circles
Figure 3: 1 + 3 x 3 = 10 circles

Formula:
Number of circles = 1 + Figure number x 3

Number of circles in Figure 20
= 1 + 20 x 3
= 61

(b)
Pattern for the total number of circles and rectangles
Figure 1: 1 + 1 x 4 = 5
Figure 2: 1 + 2 x 4 = 9
Figure 3: 1 + 3 x 4 = 13

Formula:
Total number of rectangles and circles = 1 + Figure number x 4

1 + Figure number x 4 = 157
Figure number x 4 = 157 - 1 = 156
Figure number = 156 ÷ 4 = 39

Answer(s): (a) 61; (b) 39