The graph shows 3 figures formed by shaded and white triangles.

Pattern number	1	2	3	...	8
Number of shaded triangles	0	2	5	...	(i)
Total number of triangles	1	3	8	...	(ii)

1. Complete the column for Figure 8. Give your answers for (i) and (ii) in numbers. (Eg 1, 2)
2. What is the total number of triangles in Figure 17?
3. How many shaded triangles are there in Figure 49?

(a)
Pattern for the number of shaded triangles
Figure 1: 0 = 0 = 1 - 1
Figure 2: 0 + 2 = 2 = 1 + 2 - 1
Figure 3: 0 + 2 + 3 = 5 = 1 + 2 + 3 - 1

Formula:
Number of shaded triangles = Sum of all numbers to Figure number - 1

Number of shaded triangles in Figure 8
= (1 + 2 + 3 + ... + 8) - 1
= (8 x 9 ÷ 2) - 1
= 36 - 1
= 35 (i)

Pattern for the number of triangles from Figure 2 onwards.
Figure 2: 2² - 1 = 2 x 2 - 1 = 3
Figure 3: 3² - 1 = 3 x 3 - 1 = 8 

Formula:
Number of triangles = Figure number² - 1

Total number of triangles in Figure 8
= 8² - 1
= 8 x 8 - 1
= 64 - 1
= 63 (ii)

(b)
Total number of triangles in Figure 17
= 17² - 1
= 17 x 17 - 1
= 289 - 1
= 288

(c)
Number of shaded triangles in Figure 49
= (1 + 2 + 3 + ... + 49) - 1
= (49 x 50 ÷ 2) - 1
= 1225 - 1
= 1224

Answer(s): (a) 35, 63; (b) 288; (c) 1224