See the figures made with matchsticks:
The numbers of sticks needed for the next figure is
18
No. of match sticks in fig 1 =9
No. of match sticks in fig 2 =12 =9+3
No. of match sticks in fig 3 =15 =12+3
⇒ The no of sticks are increasing by 3 in every figures.
So the no. of sticks in the next fig will be 15+3=18