Jenson formed some figures using squares and circles as shown.
- Find the number of squares in Figure 8.
- Find the total number of circles and squares in Figure 28.
- A figure in the pattern has a total of 2071 circles and squares. What is the Figure Number?
(a)
Number of squares
Figure 1: 2 = 1 + 1
Figure 2: 3 = 1 + 2
Figure 3: 4 = 1 + 3
Figure 4: 5 = 1 + 4
Formula:
Number of squares = 1 + Figure Number
Number of squares in Figure 8
= 1 + 8
= 9
(b)
Total number of circles and squares
Figure 1: 3 = 1 + 2(1)
Figure 2: 7 = 1 + 2(1 + 2)
Figure 3: 13 = 1 + 2(1 + 2 + 3)
Figure 4: 21 = 1 + 2(1 + 2 + 3 + 4)
Formula:
Number of circles and squares= 1 + 2[
12 x Figure Number x (Figure Number + 1)]
Total number of circles and squares
= 1 + 2[
12 x Figure Number x (Figure Number + 1)]
= 1 + 2(
12 x 28 x 29)
= 1 + 28 x 29
= 1 + 812
= 813
(c)
1 + 2[
12 x Figure Number x (Figure Number + 1)] = 2071
2[
12 x Figure Number x (Figure Number + 1)] = 2071 - 1
Figure Number x (Figure Number + 1) = 2070
45 x 46 = 2070
Figure number that has a total number of circles and squares = 45
Answer(s): (a) 9; (b) 813; (c) 45