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[tex]f(n)=3^n[/tex]
find expressions for [tex]f(n+3)[/tex] and [tex]f(n+1)[/tex]
hence find the value of [tex]k[/tex] such that [tex]f(n+3)-f(n+1)= kf(n)[/tex] where k ∈ N

Respuesta :

versacci24

Answer:

[tex]24(f(n))[/tex]

Step-by-step explanation:

[tex]f(n+3) = 3^{n+3}\\f(n+1) = 3^{n+1}[/tex]

so

[tex]f(n+3) - f(n+1) = 3^{n+3} - 3^{n+1}[/tex]

[tex]= 27(3^n) - 3(3^n)[/tex]

[tex]= 24(3^n)[/tex]

[tex]= 24(f(n))[/tex]

hope this helped! :)

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