The first three figures of a sequence are shown. The table records the number of shaded and unshaded rhombuses in each figure.

1. Find the number of unshaded rhombuses in Figure 8?
2. Find the number of shaded rhombuses in Figure 40?
3. Which figure number has 856 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: 1² = 1
Figure 2: 2² = 4
Figure 3: 3² = 9

Number of unshaded rhombuses = Figure number²

Number of unshaded rhombuses in Figure 8
= 8²
= 64

(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 40
= 40 x 4 + 4
= 160 + 4
= 164

(c)
Number of shaded rhombuses = Figure number x 4 + 4
Figure number = (Number of shaded rhombuses - 4) ÷ 4

Figure number with 856 shaded rhombuses
= (856 - 4) ÷ 4
= 213

Answer(s): (a) 64; (b) 164; (c) 213