Find the median of the first 50 even natural numbers.

Answer

To find the median of the first 50 even natural numbers, we can follow these steps:

### Step 1: Identify the first 50 even natural numbers.
The first 50 even natural numbers are:
2, 4, 6, 8, ..., 100.

### Step 2: Confirm the sequence of even natural numbers.
Even natural numbers can be expressed in the form of \(2n\), where \(n\) is a natural number. For the first 50 even natural numbers:
- When \(n = 1\), \(2 \times 1 = 2\)
- When \(n = 2\), \(2 \times 2 = 4\)
- ...
- When \(n = 50\), \(2 \times 50 = 100\)

Thus, the first 50 even natural numbers are indeed 2, 4, 6, ..., 100.

### Step 3: Determine the number of terms (N).
Here, \(N = 50\) (the total number of even natural numbers we are considering).

### Step 4: Calculate the median.
Since \(N\) is even, the median is calculated using the formula:
\[ \text{Median} = \frac{\text{(N/2)th term} + \text{(N/2 + 1)th term}}{2} \]
Here, \(N/2 = 25\) and \(N/2 + 1 = 26\).

### Step 5: Find the 25th and 26th terms.
- The 25th term is \(2 \times 25 = 50\).
- The 26th term is \(2 \times 26 = 52\).

### Step 6: Substitute the values into the median formula.
Now, substituting the values we found:
\[ \text{Median} = \frac{50 + 52}{2} = \frac{102}{2} = 51 \]

### Final Answer:
The median of the first 50 even natural numbers is **51**.

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