The diagram shows the pattern for the number of circles.
- How many circles will Pattern 5 contain?
- How many circles will Pattern 45 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 5: 5
2 + 5 + 1 = 31
(b)
Number of circles in Figure 45
= 45
2 + 45 + 1
= 2025 + 45 + 1
= 2071
(c)
Guess & Check
Figure number
2 + Figure number + 1 = 1407
37
2 + 37 + 1 = 1407
Figure 37 contains 1407 circles.
Answer(s): (a) 31; (b) 2071; (c) 37