Question

Instructions: Given the recursive rule, match it to the explicit form.

Answer 1

Step-by-step explanation:

If we have a recursive expression with the form

`a_n=a_(n-1)\cdot c`

Then, the explicit formula is

`a_n=a_1\cdot c^(n-1)`

Therefore, for each option, we get:

`\begin{gathered} a_n=a_(n-1)\cdot2\text{ with a}_1=1 \\ \text{ Then} \\ a_n=1\cdot2^(n-1)=2^(n-1) \end{gathered}`
`\begin{gathered} a_n=a_(n-1)\cdot-2\text{ with a}_1=2 \\ \text{ Then} \\ a_n=2\cdot(-3)^(n-1) \end{gathered}`
`\begin{gathered} a_n=a_(n-1)\cdot4\text{ with a}_1=-1 \\ \text{ Then} \\ a_n=-1\cdot4^(n-1)=-4^(n-1) \end{gathered}`
`\begin{gathered} a_n=a_(n-1)\cdot2\text{ with a}_1=-3 \\ \text{ Then} \\ a_n=-3\cdot2^(n-1) \end{gathered}`

Answer:

Therefore, the answer is: