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.