Answer: [tex]f(n)=f(n-1)-6[/tex] , where f(1)=5 and n>1.
Step-by-step explanation:
The given sequence : 5,-1,-7,-13,-19...
The first term: f(1)=5
We can see that the common difference between each term : d= -6 [-1-5=-6, -7-(-1)=-6, ...]
It mean its arithmetic sequence .
Recursive formula for arithmetic sequence :
[tex]f(n)=f(n-1)+d[/tex]
Put d= -6 , we get
[tex]f(n)=f(n-1)+(-6)\\\\ f(n)=f(n-1)-6[/tex]
i.e. Recursive formula can be used to generate the given sequence:
[tex]f(n)=f(n-1)-6[/tex] , where f(1)=5 and n>1.
