To solve this problem, we need to determine the first four terms of the sequence defined by:

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

Step-by-step solution:

• Step 1: Start with $f(1) = 27$.

• Step 2: Find $f(2)$: $f(2) = \frac{1}{3} f(1) = \frac{1}{3} \times 27 = 9$

• Step 3: Find $f(3)$: $f(3) = \frac{1}{3} f(2) = \frac{1}{3} \times 9 = 3$

• Step 4: Find $f(4)$: $f(4) = \frac{1}{3} f(3) = \frac{1}{3} \times 3 = 1$

The first four terms of the sequence are:

$27, 9, 3, 1$

Correct Answer:

A. $27, 9, 3, 1$

Would you like further clarification or details on how recursive sequences are calculated?

Here are 5 related questions you might explore:

1. How can recursive sequences be graphed for visualization?
2. What happens if we change the initial value $f(1)$ to another number?
3. How does dividing by a constant factor affect the convergence of a sequence?
4. Can this sequence be expressed in a closed-form formula?
5. How would the sequence behave if $f(n) = \frac{1}{2} f(n-1)$ instead?

Tip: When solving recursive sequences, always compute a few initial terms to identify the pattern!