Raeann uses rods and buttons to form figures that follow a pattern. The first four figures are shown.
- The table shows the number of rods and buttons Raeann used to each figure. Complete the table for Figure 5 (i) and (ii). Give your answers in the following format. (Eg 1, 2)
- A figure in the pattern has a total of 172 buttons. What is the figure number of that pattern?
- How many rods are there in Figure 20?
(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 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 rods for Figure 5
= 1 + 5 x 2
= 11
Number of buttons for Figure 5
= 2 + 5
= 7
(b)
2 + Figure Number = 172
Figure Number = 172 - 2
Figure Number = 170
Figure Number that has a total of 172 buttons: 170
(c)
Number of rods in Figure 20
= 1 + 20 x 2
= 1 + 40
= 41
Answer(s): (a) 11, 7 ; (b) 170; (c) 41