Given the problem:

• $f(1) = 6$
• $f(n) = 5f(n-1)$

We are required to find $f(6)$.

Step-by-Step Solution:

1. Find $f(2)$: $f(2) = 5f(1) = 5 \times 6 = 30$

2. Find $f(3)$: $f(3) = 5f(2) = 5 \times 30 = 150$

3. Find $f(4)$: $f(4) = 5f(3) = 5 \times 150 = 750$

4. Find $f(5)$: $f(5) = 5f(4) = 5 \times 750 = 3750$

5. Find $f(6)$: $f(6) = 5f(5) = 5 \times 3750 = 18750$

Thus, the value of $f(6)$ is $\boxed{18750}$.

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. How would the value of $f(7)$ be calculated using the same recursive formula?
2. What is the general formula for $f(n)$ in this sequence?
3. Can the sequence be expressed as a closed-form expression rather than a recursive one?
4. How does the sequence grow as $n$ increases? Is it linear, exponential, or something else?
5. How would the sequence change if the initial condition $f(1)$ were different?

Tip: In recursive sequences, understanding the base case (like $f(1)$ here) is crucial for accurately determining subsequent values.