What is the average of squares of first 10 natural numbers?

Options

A. 55.5
B. 45.6
C. 38.5
D. 40.5

Answer

To find the average of the squares of the first 10 natural numbers, we can follow these steps:

### Step 1: Identify the first 10 natural numbers
The first 10 natural numbers are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

### Step 2: Calculate the squares of these numbers
We calculate the squares:
- \(1^2 = 1\)
- \(2^2 = 4\)
- \(3^2 = 9\)
- \(4^2 = 16\)
- \(5^2 = 25\)
- \(6^2 = 36\)
- \(7^2 = 49\)
- \(8^2 = 64\)
- \(9^2 = 81\)
- \(10^2 = 100\)

### Step 3: Sum the squares
Now, we add these squares together:
\[ 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 = 385 \]

### Step 4: Calculate the average
To find the average, we divide the sum of the squares by the number of natural numbers (which is 10):
\[ \text{Average} = \frac{\text{Sum of squares}}{\text{Number of terms}} = \frac{385}{10} = 38.5 \]

### Final Answer
The average of the squares of the first 10 natural numbers is **38.5**.

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