Homework Help: math

Posted by anonymous on Thursday, October 28, 2010 at 10:28am.

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?

math - jai, Thursday, October 28, 2010 at 10:37am
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. :)

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