The following figures are made of ovals.
- How many ovals will there be in Figure 9?
- How many ovals will there be in Figure 26?
- Which figure will have 6845 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 9
= (9 - 1)
2 + 9
2= 8
2 + 9
2 = 8 x 8 + 9 x 9
= 145
(b)
Number of ovals in Figure 26
= (26 - 1)
2 + 26
2= 25
2 + 26
2 = 25 x 25 + 26 x 26
= 1301
(c)
By guess and check,
(Figure Number - 1)
2 + Figure Number
2 = 6845
58
2 + 59
2 = 6845
Figure Number = 59
Answer(s): (a) 145; (b) 1301; (c) 59
