(b) These are the first four diagrams in a sequence.
Each diagram is made from small equilateral triangles.
Diagram 1 Diagram 2
Diagram 3
(i) Write down the number of lines of symmetry of Diagram 3.
Diagram 4
3..........
.... [1]
(ii) Complete the table.
Diagram number (n)
1
2
3
4
Number of white triangles (w)
1
3
6
16
Number of grey triangles (g)
0
3
-
b
Total number of small triangles (t)
1
4
9
16
[2]
(iii) Find a formula, in terms of n, for the total number of small triangles, t, in Diagram n.
t = .....
(iv) The formula for the number of white triangles, w, in Diagram nis w = n(n+1).
.... [1]
Show that this formula gives the correct number of white triangles when n =
= 3.
(v) Complete this statement for Diagram 15.
[2]
when n= 15 w=.... g=..... and t=....​