Answer:
[tex]f(n)=f(n-1)-6[/tex], where [tex]f(1)=5[/tex] and [tex]n\:>\:1[/tex]
Step-by-step explanation:
The terms of the sequence are:
[tex]5,-1,-7,-13,-19[/tex]
The first term of this sequence is [tex]f(1)=5[/tex].
There is a constant difference among the terms.
This constant difference can determined by subtracting a previous term from a subsequent term.
[tex]d=-1-5=-6[/tex]
The general term of this arithmetic sequence is given recursively by [tex]f(n)=f(n-1)+d[/tex]
We substitute the necessary values to obtain:
[tex]f(n)=f(n-1)+-6[/tex]
Or
[tex]f(n)=f(n-1)-6[/tex], where [tex]f(1)=5[/tex] and [tex]n\:>\:1[/tex]
