Ahmad used sticks to form the following figures.

- (a)
The table shows the number of triangles and sticks for the first three figures.
Complete the table for Figure 4. - (b)
A figure in the pattern has a total of 2507 sticks.
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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 each time (, ).
For Figure 4, number of triangles = .
2. Find the number of sticks for Figure 4 by observing the constant difference
The number of sticks increases by each time (, ).
For Figure 4, number of sticks = .
Number of triangles: , Number of sticks:
13(b)
1. Find the general formula for the number of sticks in Figure $n$
The number of sticks forms an arithmetic progression:
The common difference is .
The number of sticks in Figure is .
2. Set up and solve the equation for the given number of sticks
Let .
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