Question

I need help on a problem

Answer 1

`g_n=15\cdot3^(n-1)`

1)split: 3 ´powered to n-1 is equal to 3 power to n multiplied by 3 powered to -1:

`=15\cdot3^3\cdot3^(-1)`

2) Flip: a negative expinent (x powered to -1) is equal to 1/x.

`=15\cdot3^n\cdot(1)/(3)`

3. Multiply: multiply 15 by 1/3

`\begin{gathered} =(15)/(3)\cdot3^n \\ \\ =5\cdot3^n \end{gathered}`

4. Replace: replace n by x

`f(x)=5\cdot3^x`