Study the series of figures carefully.

1. Complete the table.
2. Find the number of sticks needed in Pattern Number 30.
3. Find the number of dots needed when 511 sticks are used.

Pattern Number	Number of sticks	Number of dots
1	3	3
2	8	5
3	13	7
...	...	...
15	?	31
16	63	?

(a)
Pattern for the number of sticks
Pattern 1: 1 x 4 - 1 = 3 sticks
Pattern 2: 2 x 4 - 1 = 7 sticks
Pattern 3: 3 x 4 - 1 = 11 sticks

Formula:
Number of sticks needed = Pattern number x 4 - 1

Number of sticks needed for Pattern 15
= 15 x 4 - 1
= 59

Pattern for the number of dots
Pattern 1: 1 x 2 + 1 = 3 dots
Pattern 2: 2 x 2 + 1 = 5 dots
Pattern 3: 3 x 2 + 1 = 7 dots

Formula:
Number of dots = (Pattern Number x 2) + 1

Number of dots needed for Pattern 16
= 16 x 2 + 1
= 33

(b)
Number of sticks needed in Pattern 30
= 30 x 4 - 1
= 119

(c)
Pattern Number x 4 - 1 = 511
Pattern Number x 4 = 511 + 1 = 512
Pattern number = 512 ÷ 4 = 128

Number of dots needed in Pattern 128
= 128 x 2 + 1
= 257

Answer(s): (a) 33, 59; (b) 119; (c) 257