The first four figures of a pattern as shown.
The table shows the number of circles and squares used in each figure.
- Find the values of (i) and (ii). Give your answers in the following format. (Eg 1, 2)
- How many circles are there in Figure 40?
- How many squares are there in Figure 70?
(a)
(i)
Number of circles:
Figure 1: 5 = 2 + 1 x 3
Figure 2: 8 = 2 + 2 x 3
Figure 3: 11 = 2 + 3 x 3
Formula:
Number of circles = 2 + Figure Number x 3
Number of circles for Figure 5
= 2 + 5 x 3
= 2 + 15
= 17
(ii)
Number of squares:
Figure 1: 4 = 4 x 1
Figure 2: 12 = 4 x (1 + 2)
Figure 3: 24 = 4 x (1 + 2 + 3)
Formula:
Number of squares = 4 x
Figure Number x (Figure Number + 1) 2 Number of squares at Figure 5
= 4 x
Figure Number x (Figure Number + 1) 2= 4 x
5 x (5 + 1) 2= 4 x
5 x 6 2= 2 x 30
= 60
(b)
Number of circles in Figure 40
= 2 + 40 x 3
= 2 + 120
= 122
(c)
Number of squares in Figure 70
= 4 x
Figure Number x (Figure Number + 1) 2= 4 x
70 x (70 + 1) 2= 4 x
70 x 71 2 = 2 x 4970
= 9940
Answer(s): (a) 17, 60; (b) 122; (c) 9940