Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN: 9781133382119
Author: Swokowski
Publisher: Cengage

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Question
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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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