a) Yes
b) No
c) No
d) No
Explanation:
We check the options for the data set given:
[tex]f(1)\text{ = 9, f(2) = 45, f(3) = 225, f(4) = 1125}[/tex]
[tex]\begin{gathered} f(n)=9(5)^{n-1} \\ \text{when n = 1} \\ f(1)=9(5)^{0\text{ }}\text{ = 9} \\ \text{when n =2} \\ f(2)\text{ =}9(5)^{2-1\text{ }}=\text{ 9(5) = 45} \\ \text{when n = 3} \\ f(3)\text{ =}9(5)^{3-1\text{ }}=9(25)\text{ = 225 } \\ \text{when x = 4} \\ f(3)\text{ = }9(5)^{4-1\text{ }}=9(125)\text{ = 1125 (correct)} \\ So,\text{ Yes} \end{gathered}[/tex][tex]\begin{gathered} f(n)=5(9)^{n-1} \\ \text{when n = 1} \\ f(1)=5(9)^{1-1}=5(9)^0\text{ = 5} \\ \text{when = 2} \\ f(2)=5(9)^{2-1}=5(9)^1\text{ = 45} \\ \text{when n = 3} \\ f(3)=5(9)^{3-1}=5(9)^2\text{ = }405\text{ (wrong)} \\ \text{so, No} \end{gathered}[/tex][tex]\begin{gathered} f(n)=5(5)^{n-1} \\ \text{when n = 1} \\ f(1)=5(5)^{1-1}=5(5)^0\text{ = 5} \\ \text{when n = 2} \\ f(2)\text{ = }5(5)^{2-1}=5(5)\text{ = 25 (wrong)} \\ so,\text{ No} \end{gathered}[/tex][tex]\begin{gathered} f(n)=9(9)^{n-1} \\ \text{when n = 1} \\ f(1)\text{ = }9(9)^{1-1}=9(9)^0\text{ = 9} \\ \text{when n = 2} \\ f(2)\text{ = }9(9)^{2-1}=9(9)^1\text{ = 81 (wrong)} \\ so,\text{ No} \end{gathered}[/tex]
