Question

Find the number of vertices in the next pattern.

Answer 1

Let x = number of steps
y = number of vertices [1 mark]
Tabulating the values,

x	1	2	3	4	5
y	3	6	12	24	?

[1 mark]
Hence, the relationship between x and y can be generalised as y = 3$\times$$2^{(x-1)}$
Required number of vertices in the next pattern
= 3$\times$$2^{(5-1)}$ = 3$\times$$2^4$ = 48 [1 mark]