The following figures are made of ovals.
- How many ovals will there be in Figure 7?
- How many ovals will there be in Figure 55?
- Which figure will have 3121 ovals?
(a)
Figure 1 = 0
2 + 1
2 = 1
Figure 2 = 1
2 + 2
2 = 5
Figure 3 = 2
2+ 3
2 = 13
Figure 4 = 3
2 + 4
2 = 25
Formula:
Number of ovals = (Figure number - 1)
2 + Figure number
2Number of ovals in Figure 7
= (7 - 1)
2 + 7
2= 6
2 + 7
2 = 6 x 6 + 7 x 7
= 85
(b)
Number of ovals in Figure 55
= (55 - 1)
2 + 55
2= 54
2 + 55
2 = 54 x 54 + 55 x 55
= 5941
(c)
By guess and check,
(Figure Number - 1)
2 + Figure Number
2 = 3121
39
2 + 40
2 = 3121
Figure Number = 40
Answer(s): (a) 85; (b) 5941; (c) 40