The diagram shows the pattern for the number of circles.
- How many circles will Pattern 8 contain?
- How many circles will Pattern 47 contain?
- Which pattern contains 241 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 47
= 47
2 + 47 + 1
= 2209 + 47 + 1
= 2257
(c)
Guess & Check
Figure number
2 + Figure number + 1 = 241
15
2 + 15 + 1 = 241
Figure 15 contains 241 circles.
Answer(s): (a) 73; (b) 2257; (c) 15
