Answer: The correct option is 1, i.e., [tex]f(x+1)=\frac{5}{6}f(x)[/tex].
Explanation:
The geometric sequence is in the form of,
[tex]a,ar,ar^2,ar^3,....[/tex]
Where, a is the first term of the sequence and r is the common ratio of the sequence.
It means the [tex]n_{th}[/tex] term of the sequence is defined as,
[tex]a_n=ar^{n-1}[/tex]
So the the [tex](n+1)_{th}[/tex] term of the sequence is defined as,
[tex]a_{n+1}=ar^n[/tex]
[tex]a_{n+1}=r(ar^{n-1})[/tex]
[tex]a_{n+1}=ra_n[/tex]
It means the geometric sequence is in the form of,
[tex]f(x+1)=rf(x)[/tex]
Where, r be any constant.
From the options only [tex]f(x+1)=\frac{5}{6}f(x)[/tex] is in the form of [tex]f(x+1)=rf(x)[/tex] with common ratio [tex]\frac{5}{6}[/tex].
Therefore, the function can be used to model the graphed geometric sequence is [tex]f(x+1)=\frac{5}{6}f(x)[/tex] .
A - f(x + 1) = ⅚ f(x)
Step-by-step explanation:
Right on the edge final!
I hope this helps!
- sincerelynini
