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

1. The table shows the number of sticks and beads Gwen used to each figure. Complete the table for Figure 7 (i) and (ii). Give your answers in the following format. (Eg 1, 2)
2. A figure in the pattern has a total of 163 beads. What is the figure number of that pattern?
3. How many sticks are there in Figure 20?

(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 beads:
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 beads = 2 + Figure Number

Number of sticks for Figure 7
= 1 + 7 x 2
= 15

Number of beads for Figure 7
= 2 + 7
= 9

(b)
2 + Figure Number = 163
Figure Number = 163 - 2
Figure Number = 161

Figure Number that has a total of 163 beads: 161

(c)
Number of sticks in Figure 20
= 1 + 20 x 2
= 1 + 40
= 41

Answer(s): (a) 15, 9 ; (b) 161; (c) 41