Find the average of the square of first consecutive odd numbers starting from 1 to 9, where the last odd number is 9.

Options

A. 22
B. 11
C. 16
D. 33

Answer

To find the average of the squares of the first consecutive odd numbers starting from 1 to 9, we will follow these steps:

### Step 1: Identify the odd numbers
The first consecutive odd numbers from 1 to 9 are:
1, 3, 5, 7, 9

### Step 2: Calculate the squares of these odd numbers
Now, we will square each of these odd numbers:
- \(1^2 = 1\)
- \(3^2 = 9\)
- \(5^2 = 25\)
- \(7^2 = 49\)
- \(9^2 = 81\)

So, the squares are:
1, 9, 25, 49, 81

### Step 3: Sum the squares
Next, we will sum these squares:
\[ 1 + 9 + 25 + 49 + 81 = 165 \]

### Step 4: Count the number of odd numbers
We have a total of 5 odd numbers (1, 3, 5, 7, 9).

### Step 5: Calculate the average
To find the average, we divide the sum of the squares by the number of odd numbers:
\[ \text{Average} = \frac{\text{Sum of squares}}{\text{Number of odd numbers}} = \frac{165}{5} = 33 \]

### Final Answer
The average of the squares of the first consecutive odd numbers from 1 to 9 is **33**.

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