# Thread: Finding a recurrence relation

1. ## Finding a recurrence relation

Can anyone help me solve part b for the following problem:

a) Find the recurrence relation satisfied by an, where an 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.

b) For the situation in part (a), let bn be the number of infinite regions that result. Find the recurrence relation for bn.

I found my recurrence relation for part a, but is bn the sum of all regions found in a) or what?

2. Originally Posted by precious_pearl13
a) Find the recurrence relation satisfied by an, where an 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.

b) For the situation in part (a), let bn be the number of infinite regions that result. Find the recurrence relation for bn.

I found my recurrence relation for part a, but is bn the sum of all regions found in a) or what?
every new line adds only two new infinite regions. thus: $\displaystyle b_{n+1}=b_n + 2, \ \ n \geq 1,$ and $\displaystyle b_1=2.$ therefore: $\displaystyle b_n=2n, \ \ n \geq 1.$

3. In future, it is not necessary to tell us to delete your posts when you understand.
Rather post a message thanking the user who helped you.

(I think when you reach 10 posts you should be able to delete your own posts anyway.)