Identify the sequence graphed below and the average rate of change from n = 1 to n = 3.

Answer:The required sequence is [tex]a_n=20(\frac{1}{2})^{n-1}[/tex]. The average rate of change from n = 1 to n = 3 is -7.5.Step-by-step explanation:From the given graph it is clear that the sequence is a GP because the all terms are half of their previous terms.Here, [tex]a_2=10,a_3=5,a_4=2.5,a_5=1.25[/tex][tex]r=\frac{a_3}{a_2}=\frac{5}{10}=\frac{1}{2}[/tex]The common ratio of GP is 1/2.[tex]r=\frac{a_2}{a_1}[/tex][tex]\frac{1}{2}=\frac{10}{a_1}[/tex][tex]a_1=20[/tex]The first term of the sequence is 20.The formula for sequence is[tex]a_n=a(r)^{n-1}[/tex]Where a is first term and r is common difference.The required sequence is[tex]a_n=20(\frac{1}{2})^{n-1}[/tex]The formula for rate of change is[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]The average rate of change from n = 1 to n = 3 is[tex]m=\frac{f(3)-f(1)}{3-1}[/tex][tex]m=\frac{5-20}{3-1}[/tex][tex]m=\frac{-15}{2}=-7.5[/tex]Therefore the required sequence is [tex]a_n=20(\frac{1}{2})^{n-1}[/tex]. The average rate of change from n = 1 to n = 3 is -7.5.