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. write the summation notation that represents the total number of shaded triangles in the first 9 figures?

9841

Step-by-step explanation:

Each time the number of shaded triangles is multiplied by 3.  So this is a geometric series:

an = 1 (3)ⁿ⁻¹

The sum of the first n terms of a geometric series is:

S = a₁ (1 - rⁿ) / (1 - r)

Here, a₁ = 1, r = 3, and n = 9.

S = 1 (1 - 3⁹) / (1 - 3)

S = 9841

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