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 12?
2. Find the number of shaded rhombuses in Figure 69?
3. Which figure number has 544 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 12
= 12²
= 144

(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 69
= 69 x 4 + 4
= 276 + 4
= 280

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

Figure number with 544 shaded rhombuses
= (544 - 4) ÷ 4
= 135

Answer(s): (a) 144; (b) 280; (c) 135