Respuesta :
The correct answer is f(n + 1) = –0.5f(n) since n is greater than 1
Answer:
[tex]f(n)=-0.5\times f(n-1)[/tex]
Step-by-step explanation:
Sequence: 9.6, –4.8 , 2.4, –1.2, 0.6, ...
So, f(1) = first term = 9.6
r = common ratio = [tex]\frac{-4.8}{9.6} =\frac{2.4}{-4.8} = -0.5[/tex]
Now , formula of nth term in G.P. = [tex]f(n)=f(1)\times r^{n-1}[/tex]
So, formula for nth term of the given sequence = [tex]f(n)=9.6\times (-0.5)^{n-1}[/tex]
So, [tex]f(n-1)=9.6\times (-0.5)^{n-1-1}[/tex]
[tex]f(n-1)=9.6\times (-0.5)^{n-2}[/tex]
Recursive formula :
[tex]\frac{f(n)}{f(n-1)}= \frac{9.6\times (-0.5)^{n-1}}{9.6\times (-0.5)^{n-2}}[/tex]
[tex]\frac{f(n)}{f(n-1)}=(-0.5)^{n-1-(n-2)}[/tex]
[tex]\frac{f(n)}{f(n-1)}=(-0.5)^{-1+2}[/tex]
[tex]\frac{f(n)}{f(n-1)}=-0.5[/tex]
[tex]f(n)=-0.5\times f(n-1)[/tex]
Hence recursive formula can be used to generate the sequence shown, where f(1) = 9.6 and n > 1 is [tex]f(n)=-0.5\times f(n-1)[/tex]
