Creating Recurrence

Question

If I have an integer $n \geq1$, and I had to draw $n$ straight lines, so that no two of them are parallel as well as no three of them intersect in one single point. These lines divide the plane into regions (some are bound while others are unbounded). I have to denote the number of these regions by $R_n$. How would I create a recurrence for the numbers $R_n$ and use it to prove for $n \geq 1$, $R_n$ = $1 + n(n + 1)/2$ ?

Answer 1

Line $n$ crosses $n-1$ other lines, so creates $n$ new regions