Study the series of figures carefully.

1. Complete the table.
2. Find the number of sticks needed in Pattern Number 22.
3. Find the number of dots needed when 347 sticks are used.

Pattern Number	Number of sticks	Number of dots
1	3	3
2	8	5
3	13	7
...	...	...
11	?	23
12	47	?

(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 11
= 11 x 4 - 1
= 43

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 12
= 12 x 2 + 1
= 25

(b)
Number of sticks needed in Pattern 22
= 22 x 4 - 1
= 87

(c)
Pattern Number x 4 - 1 = 347
Pattern Number x 4 = 347 + 1 = 348
Pattern number = 348 ÷ 4 = 87

Number of dots needed in Pattern 87
= 87 x 2 + 1
= 175

Answer(s): (a) 25, 43; (b) 87; (c) 175