The following figures are made of ovals.
- How many ovals will there be in Figure 6?
- How many ovals will there be in Figure 89?
- Which figure will have 4901 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 6
= (6 - 1)
2 + 6
2= 5
2 + 6
2 = 5 x 5 + 6 x 6
= 61
(b)
Number of ovals in Figure 89
= (89 - 1)
2 + 89
2= 88
2 + 89
2 = 88 x 88 + 89 x 89
= 15665
(c)
By guess and check,
(Figure Number - 1)
2 + Figure Number
2 = 4901
49
2 + 50
2 = 4901
Figure Number = 50
Answer(s): (a) 61; (b) 15665; (c) 50
