posted by .

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 -

    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. :)

  • math -

    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?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math : Geometry : Similar triangles

    two right triangles are similar. the of the larger triangle is 4 times as long as the base of the smaller triangle. the height of the longer triangle is 16cm. the area of the smaller triangle is 6cm^2. What is the area of the long …
  2. math

    A draw contains 3 black socks and 2 white socks. A sock isdrawn at random and then replaced. Find each probability. p(2 black) p(black, then white) p(white, then black) p(2white)
  3. biology urgent

    In mice, a gene controlling coat colour has 2 alleles; B (black) and b (white). A pure breeding black mouse is crossed to a white mouse and all the offspring are black. The offspring are then crossed to white mice. The phenotypes of …
  4. Math Help

    The triangles are similar. Find the value of x. The triangles are right triangles. Triangle 1 has 18 on the left side and 24 on the left side. Triangle 2 has x on the left side and 6 on the right side. The triangles are facing each …
  5. math

    The large red equilateral triangle has sides of 8x units. The midpoints of the red triangle are joined to form the blue triangle. The midpoints of the blue triangle ate joined to form the green triangle. The process of joining midpoints …
  6. Math

    I have a triangle with equal sides. Then a s cons triangle is put in the middle so I have four triangles. Triangles are continued to be put instead so I have more and more triangles. As more triangles are added in the same space, the …
  7. math

    An equilateral triangle with a base of 20 cm and a height of 17.3 cm is divided into 4 smaller equilateral triangles. What is true about this figure?
  8. Math

    The first pattern of triangles it uses 4 matches ( 3 matches for build a triangle and 1 matches for connected to other triangles). a)Find the number of triangles if there are 100 matches?
  9. Math

    On a test I was given 2 triangles. One triangle gave measurements of all three sides as 2, 4, and 5. The next triangle had sides given 4 and 8 and it asked what the third side should be if the triangles were perpendicular. How would …
  10. Math

    Triangle ABC has coordinates A(-4,-2), B(0,-2), and C(-4,1). Triangle DEF has coordinates D(3,6), E(3,2), and F(0,2). Use coordinate geometry to determine if these two triangles are congruent. If they are not congruent, state the reason. …

More Similar Questions