Find the sum of first 84 even numbers.

Options

A. 7140
B. 7540
C. 6720
D. 8832

Answer

To find the sum of the first 84 even numbers, we can use the formula for the sum of the first \( n \) even numbers, which is given by:

\[ \text{Sum} = n \times (n + 1) \]

### Step-by-Step Solution:

1. **Identify the value of \( n \)**:
- Here, \( n = 84 \) (since we want the sum of the first 84 even numbers).

2. **Apply the formula**:
- Substitute \( n \) into the formula:
\[ \text{Sum} = 84 \times (84 + 1) \]

3. **Calculate \( 84 + 1 \)**:
- \( 84 + 1 = 85 \)

4. **Multiply \( 84 \) by \( 85 \)**:
- Now we need to calculate:
\[ 84 \times 85 \]

5. **Perform the multiplication**:
- Break it down:
\[ 84 \times 85 = 84 \times (80 + 5) = 84 \times 80 + 84 \times 5 \]
- Calculate \( 84 \times 80 \):
\[ 84 \times 80 = 6720 \]
- Calculate \( 84 \times 5 \):
\[ 84 \times 5 = 420 \]
- Add the two results:
\[ 6720 + 420 = 7140 \]

6. **Final Result**:
- The sum of the first 84 even numbers is \( 7140 \).

### Summary:
The sum of the first 84 even numbers is \( 7140 \).