Find the sum of given terms:-
251 + 252 + 253 + ............ + 259 + 260

Answer

To find the sum of the sequence 251 + 252 + 253 + ... + 259 + 260, 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, last term, and number of terms
- **First term (a)**: 251
- **Last term (l)**: 260
- **Number of terms (n)**: To find n, we can list the terms: 251, 252, 253, 254, 255, 256, 257, 258, 259, 260. This gives us a total of 10 terms.

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

### Step 3: Substitute the values into the formula
Now we can substitute the values we found into the formula:
\[ S_{10} = \frac{10}{2} \times (251 + 260) \]

### Step 4: Simplify the expression
Calculating inside the parentheses first:
\[ 251 + 260 = 511 \]
Now substituting back into the equation:
\[ S_{10} = 5 \times 511 \]

### Step 5: Calculate the final sum
Now we multiply:
\[ 5 \times 511 = 2555 \]

### Conclusion
The sum of the given terms from 251 to 260 is **2555**.

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