What is the value of 11 + 12 + 13 + ……… + 35?

Options

A. 575
B. 630
C. 585
D. 595

Answer

To find the value of \( 11 + 12 + 13 + \ldots + 35 \), we can use the formula for the sum of the first \( n \) natural numbers.

### Step-by-Step Solution:

1. **Identify the range of numbers**: We need to find the sum of numbers from 11 to 35.

2. **Use the formula for the sum of the first \( n \) natural numbers**: The formula for the sum of the first \( n \) natural numbers is given by:
\[ S_n = \frac{n(n + 1)}{2} \]
where \( S_n \) is the sum of the first \( n \) natural numbers.

3. **Calculate the sum from 1 to 35**:
We first calculate the sum of the first 35 natural numbers:
\[ S_{35} = \frac{35(35 + 1)}{2} = \frac{35 \times 36}{2} = \frac{1260}{2} = 630 \]

4. **Calculate the sum from 1 to 10**:
Next, we calculate the sum of the first 10 natural numbers:
\[ S_{10} = \frac{10(10 + 1)}{2} = \frac{10 \times 11}{2} = \frac{110}{2} = 55 \]

5. **Subtract the sum from 1 to 10 from the sum from 1 to 35**:
To find the sum from 11 to 35, we subtract the sum from 1 to 10 from the sum from 1 to 35:
\[ S_{11 \text{ to } 35} = S_{35} - S_{10} = 630 - 55 = 575 \]

6. **Final Answer**:
Therefore, the value of \( 11 + 12 + 13 + \ldots + 35 \) is \( 575 \).