Question

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?

Answer 1

9841

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

Answer 2

on e2020 its 1 option

Explanation: