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
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
3.
So the recurrence relation is