Risa uses straws and beads to form figures that follow a pattern. The first four figures are shown.
- The table shows the number of straws and beads Risa used to each figure. Complete the table for Figure 7 (i) and (ii). Give your answers in the following format. (Eg 1, 2)
- A figure in the pattern has a total of 127 beads. What is the figure number of that pattern?
- How many straws are there in Figure 14?
(a)
Number of straws:
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 straws = 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 straws for Figure 7
= 1 + 7 x 2
= 15
Number of beads for Figure 7
= 2 + 7
= 9
(b)
2 + Figure Number = 127
Figure Number = 127 - 2
Figure Number = 125
Figure Number that has a total of 127 beads: 125
(c)
Number of straws in Figure 14
= 1 + 14 x 2
= 1 + 28
= 29
Answer(s): (a) 15, 9 ; (b) 125; (c) 29