Answer :
We are given the recursive sequence defined by
$$
f(n+1) = \frac{1}{3} f(n).
$$
This can be rewritten as
$$
f(n) = 3 f(n+1).
$$
We know that
$$
f(3) = 9.
$$
Step 1: Compute $f(2)$
Since
$$
f(3) = \frac{1}{3} f(2),
$$
we can solve for $f(2)$:
$$
f(2) = 3 f(3) = 3 \times 9 = 27.
$$
Step 2: Compute $f(1)$
Similarly, using the relation
$$
f(2) = \frac{1}{3} f(1),
$$
we solve for $f(1)$:
$$
f(1) = 3 f(2) = 3 \times 27 = 81.
$$
Thus, the value of $f(1)$ is
$$
\boxed{81}.
$$
$$
f(n+1) = \frac{1}{3} f(n).
$$
This can be rewritten as
$$
f(n) = 3 f(n+1).
$$
We know that
$$
f(3) = 9.
$$
Step 1: Compute $f(2)$
Since
$$
f(3) = \frac{1}{3} f(2),
$$
we can solve for $f(2)$:
$$
f(2) = 3 f(3) = 3 \times 9 = 27.
$$
Step 2: Compute $f(1)$
Similarly, using the relation
$$
f(2) = \frac{1}{3} f(1),
$$
we solve for $f(1)$:
$$
f(1) = 3 f(2) = 3 \times 27 = 81.
$$
Thus, the value of $f(1)$ is
$$
\boxed{81}.
$$
