Question

Decide if each of the following explicit rules listed in the table below represent the given sequence.

Answer 1

a) Yes

b) No

c) No

d) No

Step-by-step explanation:

We check the options for the data set given:

`f(1)\text{ = 9, f(2) = 45, f(3) = 225, f(4) = 1125}`

`\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}`
`\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}`
`\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}`
`\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}`