Find the average of the square of first consecutive even numbers starting from 2 to 12, where the last even number is 12.

Options

A. 12.20
B. 60.66
C. 16.45
D. 17.80

Answer

To find the average of the squares of the first consecutive even numbers starting from 2 to 12, we can follow these steps:

### Step 1: Identify the even numbers
The even numbers from 2 to 12 are:
- 2, 4, 6, 8, 10, 12

### Step 2: Calculate the squares of these even numbers
Now we will square each of these even numbers:
- \(2^2 = 4\)
- \(4^2 = 16\)
- \(6^2 = 36\)
- \(8^2 = 64\)
- \(10^2 = 100\)
- \(12^2 = 144\)

### Step 3: Sum the squares
Next, we will add these squares together:
\[ 4 + 16 + 36 + 64 + 100 + 144 = 364 \]

### Step 4: Count the number of even numbers
We have a total of 6 even numbers (2, 4, 6, 8, 10, 12).

### Step 5: Calculate the average
To find the average, we divide the sum of the squares by the number of even numbers:
\[ \text{Average} = \frac{\text{Sum of squares}}{\text{Number of even numbers}} = \frac{364}{6} \approx 60.67 \]

### Final Answer
Thus, the average of the squares of the first consecutive even numbers from 2 to 12 is approximately **60.67**.

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