The average of 5 consecutive odd positive integers is 9. The least one among them is

Options

A. 5
B. 3
C. 1
D. 7

Answer

To solve the problem of finding the least of 5 consecutive odd positive integers whose average is 9, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find 5 consecutive odd positive integers whose average is 9.

2. **Set Up the Equation**:
- Let the first odd integer be represented as \( n \).
- The next consecutive odd integers can be expressed as:
- First integer: \( n \)
- Second integer: \( n + 2 \)
- Third integer: \( n + 4 \)
- Fourth integer: \( n + 6 \)
- Fifth integer: \( n + 8 \)

3. **Calculate the Average**:
- The average of these 5 integers is given by the formula:
\[ \text{Average} = \frac{\text{Sum of integers}}{\text{Number of integers}} \]
- Here, the sum of the integers is:
\[ n + (n + 2) + (n + 4) + (n + 6) + (n + 8) = 5n + 20 \]
- Therefore, the average can be expressed as:
\[ \frac{5n + 20}{5} = 9 \]

4. **Solve for \( n \)**:
- Multiply both sides by 5:
\[ 5n + 20 = 45 \]
- Subtract 20 from both sides:
\[ 5n = 25 \]
- Divide by 5:
\[ n = 5 \]

5. **Identify the Consecutive Odd Integers**:
- Now that we have \( n = 5 \), the integers are:
- First integer: \( 5 \)
- Second integer: \( 7 \)
- Third integer: \( 9 \)
- Fourth integer: \( 11 \)
- Fifth integer: \( 13 \)

6. **Find the Least Integer**:
- The least of these integers is \( 5 \).

### Final Answer:
The least of the 5 consecutive odd positive integers is **5**.

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