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1998 AJHSME Problems/Problem 23

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If the pattern in the diagram continues, what fraction of the interior would be shaded in the eighth triangle?

picture

$\text{(A)}\ \frac{3}{8}\qquad\text{(B)}\ \frac{5}{27}\qquad\text{(C)}\ \frac{7}{16}\qquad\text{(D)}\ \frac{9}{16}\qquad\text{(E)}\ \frac{11}{45}$

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