Gillian uses sticks and buttons to form figures that follow a pattern. The first four figures are shown.

1. The table shows the number of sticks and buttons Gillian used to each figure. Complete the table for Figure 9 (i) and (ii). Give your answers in the following format. (Eg 1, 2)
2. A figure in the pattern has a total of 105 buttons. What is the figure number of that pattern?
3. How many sticks are there in Figure 14?

(a)
Number of sticks:
Figure Number 1: 1 + 1 x 2 = 3
Figure Number 2: 1 + 2 x 2 = 5
Figure Number 3: 1 + 3 x 2 = 7
Figure Number 4: 1 + 4 x 2 = 9

Formula:
Number of sticks = 1 + Figure Number x 2

Number of buttons:
Figure Number 1: 2 + 1 = 3
Figure Number 2: 2 + 2 = 4
Figure Number 3: 2 + 3 = 5
Figure Number 4: 2 + 4 = 6

Formula:
Number of buttons = 2 + Figure Number

Number of sticks for Figure 9
= 1 + 9 x 2
= 19

Number of buttons for Figure 9
= 2 + 9
= 11

(b)
2 + Figure Number = 105
Figure Number = 105 - 2
Figure Number = 103

Figure Number that has a total of 105 buttons: 103

(c)
Number of sticks in Figure 14
= 1 + 14 x 2
= 1 + 28
= 29

Answer(s): (a) 19, 11 ; (b) 103; (c) 29