The sequence in the problem is defined as:

• $f(1) = 27$
• $f(n) = \frac{1}{3} f(n - 1)$ for $n > 1$.

We are asked to find the first four terms of the sequence.

Step-by-step calculation:

1. $f(1) = 27$ (Given)
2. $f(2) = \frac{1}{3} \times f(1) = \frac{1}{3} \times 27 = 9$
3. $f(3) = \frac{1}{3} \times f(2) = \frac{1}{3} \times 9 = 3$
4. $f(4) = \frac{1}{3} \times f(3) = \frac{1}{3} \times 3 = 1$

Thus, the first four terms of the sequence are:

$27, 9, 3, 1$

Correct Answer: The first option $\boxed{27, 9, 3, 1}$.

Would you like more details or have any further questions?

Here are 5 related questions you might consider:

1. How can we generalize this sequence for any $n$?
2. What type of sequence is this, and how can we classify it mathematically?
3. How do we determine the common ratio of this sequence?
4. What would be the sum of the first 10 terms of this sequence?
5. How does changing the initial term affect the rest of the sequence?

Tip: When dealing with recursive sequences, try to calculate a few terms first to see the pattern before making generalizations!