Problem:
If the pattern in the diagram continues, what fraction of the interior would be shaded in the eighth triangle?
Answer Choices:
A. 83​
B. 275​
C. 167​
D. 169​
E. 4511​
Solution:
Step1234567​Number of triangles14916253649​Number of shaded triangles0+1=11+2=31+2+3=61+2+3+4=101+2+3+4+5=151+2+3+4+5+6=211+2+3+4+5+6+7=28​
The ratio at step eight: 6428​=167​.
Answer: C​.
The problems on this page are the property of the MAA's American Mathematics Competitions
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