Refer to Figures 2 and 3 in Section 1.1. The method of successive differences can be app...

Refer to Figures 2 and 3 in Section 1.1. The method of successive differences can be applied to the sequence of interior regions,

1, 2, 4, 8, 16, 31,

to find the number of regions determined by seven points on the circle. What is the next term in this sequence? How many regions would be determined by eight points? Verify this using the formula given at the end of that section.

(Reference Figure 2 and 3)