FERMAT 2021 Problem 23

In Figure 1, three unshaded dots are arranged to form an equilateral triangle, as shown. Figure 2 is formed by arranging three copies of Figure 1 to form the outline of a larger equilateral triangle and then filling the resulting empty space with 1 shaded dot. For each integer n>2, Figure n is formed by first arranging three copies of Figure n-1 to form the outline of a larger equilateral triangle and then filling the resulting empty space in the centre with an inverted triangle of shaded dots.

The smallest value of n for which Figure n includes at least 100000 shaded dots is

Answer Choices
A. 8
B. 9
C. 10
D. 11
E. 12