Problem:
If the pattern in the diagram continues, what fraction of the interior would be shaded in the eighth triangle?
Answer Choices:
A. 83β
B. 275β
C. 167β
D. 169β
E. 4511β
Solution:
Step1234567βNumber of triangles14916253649βNumber 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=28β
The ratio at step eight: 6428β=167β.
Answer: Cβ.
The problems on this page are the property of the MAA's American Mathematics Competitions