What is the average of all natural number from 101 to 200?

Options

A. 150.5
B. 150
C. 151
D. 149.5

Answer

To find the average of all natural numbers from 101 to 200, we can follow these steps:

### Step 1: Identify the first and last terms
The first term (a) is 101, and the last term (l) is 200.

### Step 2: Use the formula for the average
The formula for the average of a series of numbers is given by:
\[ \text{Average} = \frac{\text{First Term} + \text{Last Term}}{2} \]
Substituting the values we have:
\[ \text{Average} = \frac{101 + 200}{2} \]

### Step 3: Calculate the sum of the first and last terms
Now, we calculate the sum:
\[ 101 + 200 = 301 \]

### Step 4: Divide by 2 to find the average
Next, we divide the sum by 2:
\[ \text{Average} = \frac{301}{2} = 150.5 \]

### Final Answer
Thus, the average of all natural numbers from 101 to 200 is **150.5**.

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