The sum of the expression `551 + 552 + 553 + ……+ 560` is :

Options

A. 4350
B. 5555
C. 555
D. 6060

Answer

To find the sum of the expression \( 551 + 552 + 553 + \ldots + 560 \), we can use the formula for the sum of an arithmetic series. Here are the steps to solve the problem:

### Step 1: Identify the first term, last term, and number of terms
- The first term \( a = 551 \)
- The last term \( l = 560 \)
- To find the number of terms \( n \), we can use the formula:
\[ n = l - a + 1 \]
Substituting the values:
\[ n = 560 - 551 + 1 = 10 \]

### Step 2: Use the formula for the sum of an arithmetic series
The formula for the sum \( S_n \) of the first \( n \) terms of an arithmetic series is given by:
\[ S_n = \frac{n}{2} \times (a + l) \]
Substituting the values we found:
\[ S_{10} = \frac{10}{2} \times (551 + 560) \]

### Step 3: Calculate the sum
- First, calculate \( 551 + 560 \):
\[ 551 + 560 = 1111 \]
- Now substitute this back into the sum formula:
\[ S_{10} = 5 \times 1111 = 5555 \]

### Final Answer
Thus, the sum of the expression \( 551 + 552 + 553 + \ldots + 560 \) is \( 5555 \).

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