PSLE
Andy used 2-cm rods to build some structures. The first five structures are shown.

The table shows the number of rods used for each structure and the height of each structure. 

Structure number	Number of rods	Height of the structure (cm)
1	12	2
2	20	2
3	28	4
4	33	4
5	41	6
...	...	...
8	a	b

1. Find the value of a.
2. Find the value of b.
3. What was the height of Structure 69?
4. How many rods were used to build Structure 69?

(a)
Structure 1:
Rods used = 12

Structure 2:
Rods used
= 12 + 8
= 20

Structure 3:
Rods used
= 12 + 8 + 8
= 20 + 8
= 28

Structure 4:
Rods used
= 12 + 8 + 8 + 5
= 20 + 13
= 33

Structure 5:
Rods used
= 12 + 8 + 8 + 5 + 8
= 20 + 13 + 8
= 41

Structure 6: Rods used
= 12 + 8 + 8 + 5 + 8 + 5
= 20 + 13 + 13
= 46

Number of 13s to be added to 20 to obtain the number of rods used for Structure 8
= (Structure number - 2) ÷ 2
= (8 - 2) ÷ 2
= 6 ÷ 2
= 3

Number of rods to be used for Structure 8
= 20 + 13 x 3
= 59

(b)
Height for even numbered structure = (Figure number ÷ 2) x length of each rod

Height for Structure 8
= (8 ÷ 2) x 2
= 4 x 2
= 8 cm

(c)
Height of structure
Structure 1: 2 cm = 1 x 2
Structure 2: 2 cm = 1 x 2
Structure 3: 4 cm = 2 x 2
Structure 4: 4 cm = 2 x 2
Structure 5: 6 cm = 3 x 2

Formula for odd number structure:
Height of structure = ^{(Structure number + 1)}₂ x 2

Height of structure
= ^{(69 + 1)}₂ x 2
= 70 ÷ 2 x 2
= 35 x 2
= 70 cm

(d)
Pattern for number of rods for odd numbered structure
Structure 3: 28
Structure 5: 28 + (13 x 1)
Structure 7: 28 + (13 x 2)
Structure 9: 28 + (13 x 3)

Number of 13s to be added to 28 to obtain the number of rods used for Structure 69
= (Structure number - 3) ÷ 2
= ^{(69 - 3)}₂
= 33

Number of rods used to build Structure 69
= 28 + 33 x 13
= 457

Answer(s): (a) 59; (b) 8 cm; (c) 70 cm; (d) 457