The sequence an= 27(1/3)^n-1 is graphed below. find the average rate of change between n=2 and n=4 A. - 1/4 B. 1/4 C. -4 D. 4

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asked Feb 19, 2019 126k views

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Chris McKee · Answer 1 · 2019-02-23T20:50:09+0000

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

$\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 2 &,& 9~) % (c,d) &&(~ 4 &,& 1~) \end{array} \\\\\\ % slope = m \stackrel{\textit{average rate of change}}{slope} = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-9}{4-2}\implies \cfrac{-8}{2}\implies -4$

The sequence an= 27(1/3)^n-1 is graphed below. find the average rate of change between n=2 and n=4 A. - 1/4 B. 1/4 C. -4 D. 4

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