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

1. The table shows the number of rods and beads Cindy used to each figure. Complete the table for Figure 8 (i) and (ii). Give your answers in the following format. (Eg 1, 2)
2. A figure in the pattern has a total of 140 beads. What is the figure number of that pattern?
3. How many rods are there in Figure 27?

(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 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 rods for Figure 8
= 1 + 8 x 2
= 17

Number of beads for Figure 8
= 2 + 8
= 10

(b)
2 + Figure Number = 140
Figure Number = 140 - 2
Figure Number = 138

Figure Number that has a total of 140 beads: 138

(c)
Number of rods in Figure 27
= 1 + 27 x 2
= 1 + 54
= 55

Answer(s): (a) 17, 10 ; (b) 138; (c) 55