Answer:
[tex]f(n)=f(n-1)+22[/tex].
Step-by-step explanation:
Note: In the given function it should be (n-1) instead of (n=1).
Consider the given function is
[tex]f(n)=-11+22(n-1)[/tex]
It is the explicit form of an A.P.
For [tex]n=1[/tex],
[tex]f(1)=-11+22(1-1)=-11+0=-11[/tex]
For [tex]n=2[/tex],
[tex]f(2)=-11+22(2-1)=-11+22=11[/tex]
Common difference is
[tex]d=a_2-a_1=11-(-11)=11+11=22[/tex]
The recursive formula of an A.P. is
[tex]f(n)=f(n-1)+d[/tex]
Substitute [tex]d=22[/tex] in the above formula.
[tex]f(n)=f(n-1)+(22)[/tex]
[tex]f(n)=f(n-1)+22[/tex]
Therefore, required recursive formula is [tex]f(n)=f(n-1)+22[/tex].
