the average rate of change, is pretty much just the "slope" of the graph, therefore since we know that when n = 2, y = 9, notice the point (2,9), and when n = 4, y = 1, notice the point (4,1), thus
[tex]\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ 2 &,& 9~)
% (c,d)
&&(~ 4 &,& 1~)
\end{array}
\\\\\\
% slope = m
\stackrel{\textit{average rate of change}}{slope} = m\implies
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-9}{4-2}\implies \cfrac{-8}{2}\implies -4[/tex]
