The first figure of the Sierpinski triangle has one shaded triangle. The second figure of the Sierpinski triangle has three shaded triangles. The third figure of the Sierpinski triangle has nine shaded triangles. Which summation represents the total number of shaded triangles in the first 15 figures?

Question

Jason Mckay

Mathematics

16 March, 07:06

The first figure of the Sierpinski triangle has one shaded triangle. The second figure of the Sierpinski triangle has three shaded triangles. The third figure of the Sierpinski triangle has nine shaded triangles. Which summation represents the total number of shaded triangles in the first 15 figures?

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Esther Huber · Answer 1

The given problem is a case of geometric progression with the geometric ratio of 3 from the series 1, 3, 9 ... The sum is expressed in the equation Sum = a1 (1-r^n) / (1-r), n is equal to 15, a1 is 1 and r is 3. The answer to this series on the first 15 terms is 7174453.