The sum of first 20 positive integers will be :

Options

A. 180
B. 190
C. 200
D. `210`

Answer

To find the sum of the first 20 positive integers, we can use the formula for the sum of an arithmetic progression (AP). Here’s a step-by-step solution:

### Step 1: Identify the first term (a) and the last term (l)
The first positive integer is 1, and the last positive integer in this case is 20.
- First term (a) = 1
- Last term (l) = 20

### Step 2: Determine the number of terms (n)
We need to find the sum of the first 20 positive integers, so:
- Number of terms (n) = 20

### Step 3: Use the formula for the sum of the first n terms of an AP
The formula for the sum of the first n terms (S_n) of an arithmetic progression is:
\[ S_n = \frac{n}{2} \times (a + l) \]
Where:
- \( S_n \) = sum of the first n terms
- \( n \) = number of terms
- \( a \) = first term
- \( l \) = last term

### Step 4: Substitute the values into the formula
Now, substituting the values we have:
\[ S_{20} = \frac{20}{2} \times (1 + 20) \]

### Step 5: Calculate the sum
Calculating the expression:
\[ S_{20} = 10 \times 21 \]
\[ S_{20} = 210 \]

### Conclusion
The sum of the first 20 positive integers is **210**.

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