If the average of five consecutive odd numbers is 17, then what will be the highest number among them ?

Options

A. 21
B. 25
C. 19
D. 23.5

Answer

To solve the problem, we need to find the highest number among five consecutive odd numbers given that their average is 17.

### Step-by-Step Solution:

1. **Understanding Consecutive Odd Numbers**:
Let's denote the five consecutive odd numbers. If we let the middle number be \( x \), then the five consecutive odd numbers can be represented as:
\[ (x - 4), (x - 2), x, (x + 2), (x + 4) \]

2. **Calculating the Average**:
The average of these five numbers is given by the formula:
\[ \text{Average} = \frac{\text{Sum of numbers}}{\text{Total numbers}} \]
Here, the total numbers are 5, and we know the average is 17. Therefore, we can set up the equation:
\[ \frac{(x - 4) + (x - 2) + x + (x + 2) + (x + 4)}{5} = 17 \]

3. **Simplifying the Equation**:
Now, let's simplify the sum in the numerator:
\[ (x - 4) + (x - 2) + x + (x + 2) + (x + 4) = 5x \]
So, we can rewrite our equation as:
\[ \frac{5x}{5} = 17 \]
This simplifies to:
\[ x = 17 \]

4. **Finding the Highest Number**:
Now that we have found \( x \), which is the middle number, we can find the highest number:
\[ \text{Highest number} = x + 4 = 17 + 4 = 21 \]

5. **Conclusion**:
Therefore, the highest number among the five consecutive odd numbers is:
\[ \boxed{21} \]