Question

question 23:What is the average rate of change from n = 2 to n = 3 for the sequence an = 1(3)n − 1?0.16136

Answer 1

In general, the average rate of change of a function f(x) from x=a to x=b is given by the formula below

`A.R.C=(f(b)-f(a))/(b-a)`

Thus, in our case,

`A.R.C=(a_3-a_2)/(3-2)=a_3-a_2`

Then,

`\begin{gathered} \Rightarrow A.R.C=1(3)^(3-1)-1(3)^(2-1)=3^2-3^1=9-3=6 \\ \Rightarrow A.R.C=6 \end{gathered}`

Thus, the answer is 6.