posted by anonymous .
The base in the Sierpinski triangle has 1 white triangle and zero black triangles. The first iteration has 3 white triangles and 1 black triangle. The second iteration has 9 white triangles and 4 black triangles. The third iteration has 27 white triangles and 13 black triangles. Following this pattern, how many white triangles will the 15th iteration have?
white: 3 9 27
black: 1 4 13
notice that for the white triangle,,
let n = number of terms,, if n=1 , white=3, if n=2, white=9, thus the pattern for white is
white = 3^n
for the black, notice that the next term would be the sum of previous values of both white and black,, for instance, if n=2, black=4 because 3 (number of white at n=1) plus 1 (number of black at n=1) is equal to 4,, at n=3, black = 13 because 9+4=13,, just follow this pattern until you reach n=15.
hope this helps. :)
Suppose the area of the original equilateral triangle (iteration 0) is 80 square inches. What is the area of each of the smaller triangles formed in iteration 1? How do you know?