The diagram shows the pattern for the number of circles.
- How many circles will Pattern 8 contain?
- How many circles will Pattern 36 contain?
- Which pattern contains 2163 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 8: 8
2 + 8 + 1 = 73
(b)
Number of circles in Figure 36
= 36
2 + 36 + 1
= 1296 + 36 + 1
= 1333
(c)
Guess & Check
Figure number
2 + Figure number + 1 = 2163
46
2 + 46 + 1 = 2163
Figure 46 contains 2163 circles.
Answer(s): (a) 73; (b) 1333; (c) 46