The diagram shows the pattern for the number of circles.
- How many circles will Pattern 7 contain?
- How many circles will Pattern 36 contain?
- Which pattern contains 2551 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 7: 7
2 + 7 + 1 = 57
(b)
Number of circles in Figure 36
= 36
2 + 36 + 1
= 1296 + 36 + 1
= 1333
(c)
Guess & Check
Figure number
2 + Figure number + 1 = 2551
50
2 + 50 + 1 = 2551
Figure 50 contains 2551 circles.
Answer(s): (a) 57; (b) 1333; (c) 50