Question

F(n) = -11 + 22(n = 1) Complete the recursive formula of f(n). f(1) = f(n) = f(n - 1)+

Answer 1

Answer:

$f(n)=f(n-1)+22$.

Step-by-step explanation:

Note: In the given function it should be (n-1) instead of (n=1).

Consider the given function is

$f(n)=-11+22(n-1)$

It is the explicit form of an A.P.

For $n=1$,

$f(1)=-11+22(1-1)=-11+0=-11$

For $n=2$,

$f(2)=-11+22(2-1)=-11+22=11$

Common difference is  

$d=a_2-a_1=11-(-11)=11+11=22$

The recursive formula of an A.P. is

$f(n)=f(n-1)+d$

Substitute $d=22$ in the above formula.

$f(n)=f(n-1)+(22)$

$f(n)=f(n-1)+22$

Therefore, required recursive formula is $f(n)=f(n-1)+22$.