Respuesta :

[tex]g_n=15\cdot3^{n-1}[/tex]

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

[tex]=15\cdot3^3\cdot3^{-1}[/tex]

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

[tex]=15\cdot3^n\cdot\frac{1}{3}[/tex]

3. Multiply: multiply 15 by 1/3

[tex]\begin{gathered} =\frac{15}{3}\cdot3^n \\ \\ =5\cdot3^n \end{gathered}[/tex]

4. Replace: replace n by x

[tex]f(x)=5\cdot3^x[/tex]