Vanessa uses rods and coins to form figures that follow a pattern. The first four figures are shown.

1. The table shows the number of rods and coins Vanessa used to each figure. Complete the table for Figure 5 (i) and (ii). Give your answers in the following format. (Eg 1, 2)
2. A figure in the pattern has a total of 122 coins. What is the figure number of that pattern?
3. How many rods are there in Figure 11?

(a)
Number of rods:
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 rods = 1 + Figure Number x 2

Number of coins:
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 coins = 2 + Figure Number

Number of rods for Figure 5
= 1 + 5 x 2
= 11

Number of coins for Figure 5
= 2 + 5
= 7

(b)
2 + Figure Number = 122
Figure Number = 122 - 2
Figure Number = 120

Figure Number that has a total of 122 coins: 120

(c)
Number of rods in Figure 11
= 1 + 11 x 2
= 1 + 22
= 23

Answer(s): (a) 11, 7 ; (b) 120; (c) 23