The first three figures of a sequence are shown. The table records the number of shaded and unshaded rhombuses in each figure.
- Find the number of unshaded rhombuses in Figure 11?
- Find the number of shaded rhombuses in Figure 52?
- Which figure number has 852 shaded rhombuses?
Figure number |
Number of unshaded rhombuses |
Number of shaded rhombuses |
1 |
1 |
8 |
2 |
4 |
12 |
3 |
9 |
16 |
(a)
Pattern for the number of unshaded rhombuses
Figure 1: 1
2 = 1
Figure 2: 2
2 = 4
Figure 3: 3
2 = 9
Number of unshaded rhombuses = Figure number
2 Number of unshaded rhombuses in Figure 11
= 11
2 = 121
(b)
Pattern for the number of shaded rhombuses
Figure 1: 1 x 4 + 4 = 8
Figure 2: 2 x 4 + 4 = 12
Figure 3: 3 x 4 + 4 = 16
Number of shaded rhombuses = Figure number x 4 + 4
Number of shaded rhombuses in Figure 52
= 52 x 4 + 4
= 208 + 4
= 212
(c)
Number of shaded rhombuses = Figure number x 4 + 4
Figure number = (Number of shaded rhombuses - 4) ÷ 4
Figure number with 852 shaded rhombuses
= (852 - 4) ÷ 4
= 212
Answer(s): (a) 121; (b) 212; (c) 212