CBSE Class 8 Mathematics
Question 2 of 9
Exploring Some Geometric Themes — Question 2
Back to all questions 2
Question Find the number of holes and the triangles that remain at each step of the shape sequence that leads to the Sierpinski Triangle.
Number of holes in Step 0: 0 hole Step 1: 1 hole Step 2: 1 + 3 = 4 holes Step 3: 1 + 3 + 9 = 13 holes Step 4: 1 + 3 + 9 + 27 = 40 holes . . . Step n: \(3^{1-1}+3^{2-1}+3^{3-1}+\ldots+3^{n-1}\) holes \(3^0+3^1+3^2+\ldots+3^{n-1}\) holes