The following figures are made of ovals.
- How many ovals will there be in Figure 8?
- How many ovals will there be in Figure 39?
- Which figure will have 1861 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 8
= (8 - 1)
2 + 8
2= 7
2 + 8
2 = 7 x 7 + 8 x 8
= 113
(b)
Number of ovals in Figure 39
= (39 - 1)
2 + 39
2= 38
2 + 39
2 = 38 x 38 + 39 x 39
= 2965
(c)
By guess and check,
(Figure Number - 1)
2 + Figure Number
2 = 1861
30
2 + 31
2 = 1861
Figure Number = 31
Answer(s): (a) 113; (b) 2965; (c) 31