The sum (101+102+103+……..+200) is equal to

Options

A. 15000
B. 15025
C. 15050
D. 25000

Answer

To find the sum of the series from 101 to 200, we can use the formula for the sum of an arithmetic series. Here’s how to solve it step by step:

### Step 1: Identify the first term (A), last term (L), and number of terms (n).
- The first term \( A = 101 \)
- The last term \( L = 200 \)

### Step 2: Calculate the number of terms (n).
The number of terms in the series can be calculated using the formula:
\[ n = L - A + 1 \]
Substituting the values:
\[ n = 200 - 101 + 1 = 100 \]

### Step 3: Use the formula for the sum of an arithmetic series.
The formula for the sum \( S \) of the first \( n \) terms of an arithmetic series is:
\[ S = \frac{n}{2} \times (A + L) \]
Substituting the values we have:
\[ S = \frac{100}{2} \times (101 + 200) \]

### Step 4: Simplify the expression.
Calculating further:
\[ S = 50 \times (301) \]

### Step 5: Calculate the final sum.
Now, we multiply:
\[ S = 50 \times 301 = 15050 \]

Thus, the sum \( (101 + 102 + 103 + \ldots + 200) \) is equal to **15050**.

---