The key features that are unique to the the graphs of sequences and series is that they are discrete.
That means that the graph is not a continuos line or curve that join all the points. On the contrary, the graph is a set of separated dots, because the values are valid only for specific points.
Regarding the average rate of change, there is not difference to calculate it respect to other graphs.
The average rate of change between points is yet the slope of the line (in this case imaginary line) that joined the first and the last point, and that is:
rise y2 - y1
average rate of change = slope = ------------ = --------------
run x2 - x1