Each successive figure below is made of small triangles like the first one in the sequence. Conjecture the number of small triangles needed to make a. the 100th​ figure? b. the nth​ figure?The first figure is an equilateral triangle. In the second figure, lines parallel to each side bisect the other two sides, forming 4 equilateral triangles. In the third figure, two lines parallel to each side of the triangle trisect each side and form a total of 9 small equilateral triangles.a. How many small triangles are needed to make the 100th​ figure?It would require ? small trianglesb. How many small triangles are needed to make the nth​ figure?It would require _ small triangles.

Question

Each successive figure below is made of small triangles like the first one in the sequence. Conjecture the number of small triangles needed to make a. the 100th​ figure? b. the nth​ figure?
The first figure is an equilateral triangle. In the second figure, lines parallel to each side bisect the other two sides, forming 4 equilateral triangles. In the third figure, two lines parallel to each side of the triangle trisect each side and form a total of 9 small equilateral triangles.
a. How many small triangles are needed to make the 100th​ figure?
It would require ? small triangles
b. How many small triangles are needed to make the nth​ figure?
It would require _ small triangles.

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