Answer: The correct option is
(B) [tex]f(n+1)=f(n)-5.[/tex]
Step-by-step explanation: We are given to select the correct recursive formula that can be used to generate the following sequence :
[tex]f(1)=6,n\geq1,\\\\6,1,-4,-9,-14,...[/tex]
Let f(n) denote the nth term of the given sequence. Then, we note that
[tex]f(1)=6,\\\\f(2)=1=6-5=f(1)-5,\\\\f(3)=-4=1-5=f(2)-5,\\\\f(4)=-9=-4-5=f(3)-5,\\\\f(5)=-14=-9-5=f(4)-5,\cdots[/tex]
Therefore, the recursive formula can be written as :
[tex]f(n+1)=f(n)-5.[/tex]
Thus, the required recursive formula is [tex]f(n+1)=f(n)-5.[/tex]
Option (B) is CORRECT.
