Question

A Sierpinski triangle can be created by starting with an equilateral triangle, breaking the triangle into 4 congruent equilateral triangles, and then removing the middle triangle.
Starting from a single black equilateral triangle with an area of 256 square inches. Repeat this 5 times

Answer 1

Answer:

number of shades triangles 1,3,9,27,81,243 (multiply 3)

area of each shaded triangle in square inches 256,64,16,4,1,.25(divide by 4)

Step-by-step explanation:

Answer 2

A geometric sequence is given by multiplying the previous term by a constant

Question: The missing part of the question appear to be the following;

Part A

Complete the following table;

$\begin{array}{|c|c|c|}Step \ number &Number \ of \, shaded \ triangles& Each \ shaded \ triangle \ area \ (in^2) \\&& \\0&1&256\\ &&\\1&3&64 \\ &&\\2&9&16 \\&& \\3&27&4 \\&&\\4&81&1 \\&&\\5&243&\dfrac{1}{4} \end{array}\right]$

Part B

(i) To graph the number of shaded triangles as function of the step number

Please find attached the required graph created with MS Excel

(i) To graph the each shaded triangle area as function of the step number

Please find attached the required graph created with MS Excel

Part C

The similarities in the graphs are;

• The domains of the graphs are equal to 0 ≤ x ≤ 5

• The ranges of the graphs are approximately equal

• The graphs appear to to be a reflection across the y-axis

The difference in the graphs are;

• The graph of the number of shaded triangles as function of the step has the shape of an inverse proportional relationship

• The graph of each shaded triangle area as function of the step number has the shape of an exponential relation

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