When looking at common differences seems to lead nowhere it is also a good idea to look at common ratios as well.

A convex polygon is a polygon where all of its diagonals lie inside of it. Remember, a diagonal is a line segment obtained by joining the vertices of the polygon. The sequence is then the number of diagonals of a polygon of $n$ sides. A triangle has no diagonals, so $d_0 = 0$. A quadrilateral has two diagonals, so $d_4= 2$.

In problem 5.28, note the third differences are not all 0, so  the sequence will not be given by a quadratic function. (Hint: compare with problem 5.8)