The arithmetic mean of first 50 odd natural numbers is :

Options

A. 50
B. 625
C. 175
D. None of these

Answer

To find the arithmetic mean of the first 50 odd natural numbers, we can follow these steps:

### Step 1: Identify the first 50 odd natural numbers
The first 50 odd natural numbers are:
1, 3, 5, 7, ..., 99

### Step 2: Use the formula for the sum of the first n odd natural numbers
The sum of the first n odd natural numbers is given by the formula:
\[ \text{Sum} = n^2 \]
For our case, \( n = 50 \):
\[ \text{Sum} = 50^2 = 2500 \]

### Step 3: Calculate the arithmetic mean
The arithmetic mean (average) is calculated by dividing the sum by the number of terms:
\[ \text{Mean} = \frac{\text{Sum}}{n} \]
Substituting the values we have:
\[ \text{Mean} = \frac{2500}{50} = 50 \]

### Final Answer
The arithmetic mean of the first 50 odd natural numbers is **50**.

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