Joelle uses sticks to form figures that follow a pattern. The first five figures are shown.
- The table shows the number of sticks used for each figure. What is the number of sticks used for Figure 6?
- What is the difference in the number of sticks Joelle would use for Figure 17 and Figure 18?
- In which figure number would Joelle use 77 sticks?
(a)
Number of sticks used:
Figure 1: 1 + 3 = 4
Figure 2: 1 + 3 + 3 = 7
Figure 3: 1 + 3 + 3 + 3 = 10
Figure 4: 1 + 3 + 3 + 3 + 2 = 12
Figure 5: 1 + 3 + 3 + 3 + 2 + 3 = 15
Figure 6: 1 + 3 + 3 + 3 + 2 + 3 + 2 = 17
Figure 7: 1 + 3 + 3 + 3 + 2 + 3 + 2 + 3 = 20
Number of sticks used for Figure 6 = 17
(b)
Increase in the number of sticks that Joelle would use from Figure 5 onwards between one
odd-numbered pattern to the next consecutive
even-numbered pattern = 2
Difference in the number of sticks that Joelle would use between Figure 17 and Figure 18 = 2
(c)
Number of sticks used for
even-numbered figures from Figure 4 onwards:
Figure 4: 12 = 4 x 2.5 + 2
Figure 6: 17 = 6 x 2.5 + 2
Formula:
Number of sticks used for
even-numbered figures from Figure 4 onwards = Figure number x 2.5 + 2
Number of sticks used for
odd-numbered figures from Figure 5 onwards:
Figure 5: 15 = 5 x 2.5 + 2.5
Figure 7: 20 = 7 x 2.5 + 2.5
Formula:
Number of sticks used for
odd-numbered figures from Figure 5 onwards = Figure number x 2.5 + 2.5
Number of sticks used for
even-numbered figures from Figure 4 onwards has a remainder of 2 when divided by 2.5.
Number of sticks used for
odd-numbered figures from Figure 5 onwards has no remainder when divided by 2.5.
77 ÷ 2.5 = 30 r 2
Since the remainder is 2, the figure number is an
even number. So, we will apply the formula for the number of sticks for
even-numbered figures.
Figure number x 2.5 + 2 = 77
Figure number x 2.5 = 77 - 2
Figure number x 2.5 = 75
Figure number = 75 ÷ 2.5
Figure number = 30
Answer(s): (a) 17; (b) 2; (c) 30