The diagram shows the pattern for the number of circles.
- How many circles will Pattern 4 contain?
- How many circles will Pattern 33 contain?
- Which pattern contains 1407 circles?
(a)
Pattern for the number of circles
Figure 1: 1
2 + 1 + 1 = 3
Figure 2: 2
2 + 2 + 1 = 7
Figure 3: 3
2 + 3 + 1 = 13
Formula
Number of circles = Figure number
2 + Figure number + 1
Figure 4: 4
2 + 4 + 1 = 21
(b)
Number of circles in Figure 33
= 33
2 + 33 + 1
= 1089 + 33 + 1
= 1123
(c)
Guess & Check
Figure number
2 + Figure number + 1 = 1407
37
2 + 37 + 1 = 1407
Figure 37 contains 1407 circles.
Answer(s): (a) 21; (b) 1123; (c) 37