If f, of, 1, equals, 8*f*(1)=8 and f, of, n, equals, f, of, n, minus, 1, plus, 4*f*(*n*)=*f*(*n*−1)+4 then find the value of f, of, 6*f*(6).

Answer

Attempt 1 out of 2

To find \( f(6) \), we need to use the recursive relationship provided:

- \( f(1) = 8 \)
- \( f(n) = f(n-1) + 4 \) for \( n > 1 \)

### Step-by-step Calculation:

1. **Given:** \( f(1) = 8 \)
2. **Find \( f(2) \):**
   \[
   f(2) = f(1) + 4 = 8 + 4 = 12
   \]
3. **Find \( f(3) \):**
   \[
   f(3) = f(2) + 4 = 12 + 4 = 16
   \]
4. **Find \( f(4) \):**
   \[
   f(4) = f(3) + 4 = 16 + 4 = 20
   \]
5. **Find \( f(5) \):**
   \[
   f(5) = f(4) + 4 = 20 + 4 = 24
   \]
6. **Find \( f(6) \):**
   \[
   f(6) = f(5) + 4 = 24 + 4 = 28
   \]

### Final Answer:
\[
f(6) = 28
\]

Would you like further clarification on any step?

Here are 5 questions based on this solution:

1. What is the recursive function formula used here?
2. Can you find \( f(7) \) using the same method?
3. How would the function change if the increment was 5 instead of 4?
4. Can you generalize the function for \( f(n) \)?
5. How does recursion help in defining functions like this?

**Tip:** Recursive formulas break down a problem into smaller instances, simplifying complex calculations.

If f(1) = 8 and f(n) = f(n-1) + 4, then find the value of f(6).

Discover how to solve the recursive function f(1) = 8 and f(n) = f(n-1) + 4 to find the value of f(6). This detailed step-by-step solution covers key algebraic concepts, including recursion and sequences. Ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation