If f, of, 1, equals, 5f(1)=5 and f, of, n, equals, 5, f, of, n, minus, 1f(n)=5f(n−1) then find the value of f, of, 6f(6).

The problem states that \( f(1) = 5 \) and gives a recursive relation for \( f(n) \) as follows:

\[
f(n) = 5 f(n - 1)
\]

We are asked to find the value of \( f(6) \).

### Step-by-Step Solution
Using the given information and the recursive formula, let's find the values of \( f(2) \), \( f(3) \), \( f(4) \), \( f(5) \), and \( f(6) \).

1. **Given:** \( f(1) = 5 \).
2. **Find \( f(2) \):**
   \[
   f(2) = 5 \cdot f(1) = 5 \cdot 5 = 25
   \]
3. **Find \( f(3) \):**
   \[
   f(3) = 5 \cdot f(2) = 5 \cdot 25 = 125
   \]
4. **Find \( f(4) \):**
   \[
   f(4) = 5 \cdot f(3) = 5 \cdot 125 = 625
   \]


If f(1) = 5 and f(n) = 5 * f(n - 1), then find the value of f(6).

Learn to solve a recursive function problem where f(1) = 5 and f(n) = 5 * f(n - 1). This solution provides a step-by-step method to find f(6), covering recursion concepts and function application, ideal for Grades 10-12.

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