8. January 2007 A large equilateral triangle is sub-divided into a set of smaller equilateral triangles by the following procedure: The midpoints of the sides of each equilateral triangle are joined to form a new set of smaller triangles. The procedure is repeated m times. The table below shows the results when the above procedure has been repeated twice, that is, when n = 2. (i) Calculate the number of triangles formed when n=3. n Result after each step No. of triangles formed 1 (2 marks) 0 (ii) Determine the number of triangles formed when n=6. (2 marks) 1 A shape has 65 536 small triangles. 2 (iii) Calculate the value of n. (3 marks) 16 2 (i) 3 (ii) 64 6 (iv) Determine the number of small triangles in a shape after carrying out the procedure times. (3 marks) (iii) m 65536 (iv) 2014 ル 131 Total 10 mark