Answer:
(a) 51
(b)
(c) 20th figure
Step-by-step explanation:
The diagram is attached below.
The first triangle is formed using 6 toothpicks.
The second triangle is formed using 11 toothpicks.
The third triangle is formed using 16 toothpicks.
So, there is an increases of 5 toothpicks every time.
We can say that the number of toothpicks used to form <em>n</em> triangles are following an arithmetic progression with the first term as 6 and the common difference as 5.
The nth term will be:
(a)
Compute the number of toothpicks required for the 10th figure as follows:
Thus, the number of toothpicks required for the 10th figure is 51.
(b)
Compute the number of toothpicks required for the nth figure as follows:
(c)
Compute the value of <em>n</em> for as follows:
Thus, the 20th figure will require exactly 102 toothpicks.