Find the recurrence relation satisfied by rn, where rn is the number of regions that a plane is divided into by n lines, if no two of the lines are parallel and no three of the lines go through the same point.

1. Take a look at the pictures attached.

2. 

i) the first line divides the plane into 2 regions 

ii) the second line adds 2 more regions so we have 4 in total.

iii) the third line adds 3 more regions, so 4+3=7 regions

iv) the fourth line adds 4 more regions.

so the  line adds n more regions to the ones created by the previous n-1 lines.

3. 











So the recurrence relation is