Seven consecutive odd numbers. The average of the three middle numbers = 17. Find the average of the first 3 numbers.

Let the seven consecutive odd numbers be represented as \( x-3, x-2, x-1, x, x+1, x+2, x+3 \).

### Step 1: Given information
The average of the three middle numbers (\( x-1, x, x+1 \)) is given as 17. Therefore:

\[
\text{Average of three middle numbers} = \frac{(x-1) + x + (x+1)}{3} = 17
\]

Simplify:
\[
\frac{3x}{3} = 17 \implies x = 17
\]

### Step 2: Find the first three numbers
The first three numbers are \( x-3, x-2, x-1 \). Substituting \( x = 17 \):
\[
x-3 = 14, \quad x-2 = 15, \quad x-1 = 16
\]

### Step 3: Average of the first three numbers
The average is:
\[
\text{Average} = \frac{(x-3) + (x-2) + (x-1)}{3} = \frac{14 + 15 + 16}{3} = \frac{45}{3} = 15
\]

### Final Answer:
The average of the first three numbers is **15**.

Would you like a deeper explanation or have more questions? 

### Relative Questions:
1. What if the seven consecutive numbers were even instead of odd?
2. How does changing the middle average affect the average of the first three numbers?
3. Can you derive the average formula for any set of consecutive numbers?
4. How would the result differ if the sequence included fractions?
5. How does this concept apply to real-world data scenarios?

### Tip:
For any sequence of consecutive odd or even numbers, the middle number equals the overall average of the entire sequence!

Solve the problem of finding the average of the first three numbers in a sequence of seven consecutive odd numbers, given that the average of the three middle numbers is 17. Detailed step-by-step solution included. Ideal for students in Grades 6-8.

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