One such fractal is the Sierpinski Triangle. This fractal is created by connecting the midpoints of the three sides of an equilateral triangle. This creates a new equilateral triangle which is then "removed" from the original. The remaining three triangles are smaller versions of our original. This process can then be repeated to continue to create other iterations of the figure. The first three stages are shown here: Stage 1 Stage 2 Stage 3 Part 1: a) Write a sequence to represent how many shaded triangles there are at each stage. b) Based on this sequence, write a formula for the n" term of the sequence. c) Using at least two sentences, describe what is represented by each term in the sequence. Part II: Assume the original triangle in stage 1 had a side length of one. ) Write a formula that would give the length of a side of one of the triangles at the n" stage. If we look at the stage 1 triangle, we can find its area by multiplying one-half times the length of its base times the length of its height. Assume again that it has a side length of one. b) Find the height of the triangle in stage 1. c) Find the area of the triangle in stage 1. Part Ill: The stage 2 triangle has side length one-half. a) Find the height of one of the triangles in stage 2. b) Find the area of one of the triangles in stage 2. Be sure to simplify. Part IV: a) Use your knowledge of geometric sequences and your answers from (c) in Part II and (b) in Part Ill to write a formula for the area of one of the triangles at the no stage. b) Use your answers from (b) in Part I and (a) in Part IV to write a formula for the total area of all the shaded triangles at the n' stage. Be sure to simplify. c) Using at least three complete sentences: a. Describe what is happening to the triangle as n gets infinitely large. b. Discuss what value you believe the total shaded area will approach and why