Question

A sequence is defined by the recursive function f(n+1)=f(n). If f(3)=9, what is f(1)?

Answer 1

Put n=2 ,
f(2+1) = f(2) => f(3) = f(2) = 9
now, put n=1,
f(1+1) = f(1) => f(2) = f(1) = 9

Answer 2

Answer:  The required value of f(1) is 9.

Step-by-step explanation:  Given that a sequence is defined by the following recursive function :

$f(n+1)=f(n)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

and f(3) = 9.

We are to find the value of f(1).

Putting n = 2 in equation (i), we have

$f(2+1)=f(2)\\\\\Rightarrow f(3)=f(2).$

Since f(3) = 9, so we get

$f(2)=9.$

Again, putting n = 1 in equation (i), we get

$f(1+1)=f(1)\\\\\Rightarrow f(2)=f(1).$

Since f(2) = 9, so we arrive at

$f(1)=9.$

Thus, the required value of f(1) is 9.