The diagram shows the pattern for the number of circles.
- How many circles will Pattern 7 contain?
- How many circles will Pattern 25 contain?
- Which pattern contains 1807 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 25
= 25
2 + 25 + 1
= 625 + 25 + 1
= 651
(c)
Guess & Check
Figure number
2 + Figure number + 1 = 1807
42
2 + 42 + 1 = 1807
Figure 42 contains 1807 circles.
Answer(s): (a) 57; (b) 651; (c) 42