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 12?
- How many squares are there in Figure 49?
(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 6
= 2 + 6 x 3
= 2 + 18
= 20
(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 6
= 4 x
Figure Number x (Figure Number + 1) 2= 4 x
6 x (6 + 1) 2= 4 x
6 x 7 2= 2 x 42
= 84
(b)
Number of circles in Figure 12
= 2 + 12 x 3
= 2 + 36
= 38
(c)
Number of squares in Figure 49
= 4 x
Figure Number x (Figure Number + 1) 2= 4 x
49 x (49 + 1) 2= 4 x
49 x 50 2 = 2 x 2450
= 4900
Answer(s): (a) 20, 84; (b) 38; (c) 4900