Define a sequence c0, c1, c2, … of pictures recursively as follows: For all integers i ≥ 1      Initial Conditions, c0 = an upright equilateral triangle ?.      Recurrence Relation, ci = in centre of each upright equilateral triangle in ci-1, draw an upside down equilateral triangle ?  such that its corners touch the edges of the upright one. Draw the first 4 iterations, starting with c0. You may want to draw c3 large. Each should be a separate drawing. Get your work checked by an IA/TA/Instructor. Count the total # of triangles for each iteration in a). Note: Triangles can be of any orientation. Only count the individual triangles. Do not count a triangle which has triangles inside it. Determine T(0), the # of triangles in the 0th term. Determine the recurrence relation, T(n), that gives the # of triangles in the nth term, for n ≥ 1.

Define a sequence c₀, c₁, c₂, … of pictures recursively as follows:
For all integers i ≥ 1
     Initial Conditions, c₀ = an upright equilateral triangle ?.
     Recurrence Relation, c_i = in centre of each upright equilateral triangle in c_i-1, draw an upside down equilateral triangle ?  such that its corners touch the edges of the upright one.

1. Draw the first 4 iterations, starting with c₀. You may want to draw c₃ large. Each should be a separate drawing.
   Get your work checked by an IA/TA/Instructor.
2. Count the total # of triangles for each iteration in a).
   Note: Triangles can be of any orientation.
   Only count the individual triangles. Do not count a triangle which has triangles inside it.
3. Determine T(0), the # of triangles in the 0th term.
4. Determine the recurrence relation, T(n), that gives the # of triangles in the nth term, for n ≥ 1.