Ahmad used sticks to form the following figures.

  1. (a)

    The table shows the number of triangles and sticks for the first three figures.
    Complete the table for Figure 4.

  2. (b)

    A figure in the pattern has a total of 2507 sticks.
    What is the Figure Number?

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Worked solution

13(a)

1. Find the number of triangles for Figure 4 by observing the constant difference

The number of triangles increases by 22 each time (4−2=24 - 2 = 2, 6−4=26 - 4 = 2).
For Figure 4, number of triangles = 6+2=86 + 2 = 8.

2. Find the number of sticks for Figure 4 by observing the constant difference

The number of sticks increases by 77 each time (15−8=715 - 8 = 7, 22−15=722 - 15 = 7).
For Figure 4, number of sticks = 22+7=2922 + 7 = 29.

Answer

Number of triangles: 88, Number of sticks: 2929

13(b)

1. Find the general formula for the number of sticks in Figure $n$

The number of sticks forms an arithmetic progression: 8,15,22,…8, 15, 22, \dots
The common difference is 15−8=715 - 8 = 7.
The number of sticks in Figure nn is 8+7(n−1)=7n+18 + 7(n - 1) = 7n + 1.

2. Set up and solve the equation for the given number of sticks

Let 7n+1=25077n + 1 = 2507.
7n=25067n = 2506
n=25067=358n = \frac{2506}{7} = 358

Answer

358358

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