The average of nine consecutive odd numbers is 53. The least odd number is:

Options

A. 22
B. 27
C. 35
D. 45

Answer

To find the least odd number among nine consecutive odd numbers with an average of 53, we can follow these steps:

### Step 1: Understand the Concept of Average
The average of a set of numbers is calculated by dividing the sum of those numbers by the count of the numbers. In this case, we have nine consecutive odd numbers.

**Hint:** Remember that the average of a series of consecutive numbers can be found by identifying the middle number.

### Step 2: Identify the Middle Number
Since there are nine consecutive odd numbers, the average will be the middle number. For nine numbers, the middle number is the 5th number in the sequence.

**Hint:** The middle number in a sequence of nine numbers is the 5th number.

### Step 3: Set Up the Sequence
Let’s denote the least odd number as \( x \). The nine consecutive odd numbers can be represented as:
- \( x \) (1st number)
- \( x + 2 \) (2nd number)
- \( x + 4 \) (3rd number)
- \( x + 6 \) (4th number)
- \( x + 8 \) (5th number)
- \( x + 10 \) (6th number)
- \( x + 12 \) (7th number)
- \( x + 14 \) (8th number)
- \( x + 16 \) (9th number)

**Hint:** Consecutive odd numbers can be represented by adding 2 to each previous number.

### Step 4: Find the 5th Number
The 5th number in this sequence is \( x + 8 \). Since we know the average is 53, we can set up the equation:
\[ x + 8 = 53 \]

**Hint:** The average is equal to the middle number in a sequence of consecutive numbers.

### Step 5: Solve for \( x \)
Now, we can solve for \( x \):
\[ x + 8 = 53 \]
Subtract 8 from both sides:
\[ x = 53 - 8 \]
\[ x = 45 \]

**Hint:** To isolate \( x \), perform the opposite operation of addition, which is subtraction.

### Step 6: Conclusion
The least odd number is \( x = 45 \).

**Final Answer:** The least odd number is **45**.