A geometric sequence

Question 1 (30 marks)
Given the sets  and

set

(i)     List the first 10 elements of set A.                                                         [5 marks]
(ii)    List the first 10 elements of set B.                                                         [5 marks]
(iii)   List the elements of set C.                                                                     [5 marks]
(iii)   Draw a Venn diagram to illustrate .                         [5 marks]

(iv)   Insert any common elements in the Venn diagram  of part (iii).     [10 marks]

[Note: elements in a Venn diagram has to be indicated by a dot, together with the element, as shown, ” ]

 

 

 

Question 2 (30 marks)
Follow the instructions below …..

  • Draw an equilateral triangle of sides about 4 cm, naming the vertices as A, B and C.
    [You may use MS Word to ‘draw’, no need to be exactly equilateral, but close to one.]
  • Copy and paste triangle in (i) and draw an inverted equilateral triangle inside it using the mid-points of AB, BC and CA as vertices. Name this triangle PQR.
  • Copy and paste the result shape in (ii) and draw another equilateral triangle inside triangle PQR, naming this triangle LMN where L, M and N are the mid-points of the sides of triangle PQR.
  • Now, count the number of triangles in each of the diagrams in (i), (ii) and (iii) and write down the answers next to the diagrams.
  • Can you predict the number of triangles in the next 2 diagrams if you were to continue the process of drawing equilateral triangle within the inner most triangle.

 

  • List the five numbers in a horizontal manner; what type of sequence does the 5 numbers above constitute?

 

Use the information to find the number of triangles after adding the 10th triangle.
 

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