The average of seven consecutive even natural numbers is 36 . The value of the first number is

Options

A. 26
B. 30
C. 32
D. 28

Answer

To solve the problem step by step, we can follow these instructions:

1. **Understand the Problem**: We need to find the first of seven consecutive even natural numbers whose average is 36.

2. **Set Up the Variables**:
Let the first even natural number be \( x \). Therefore, the seven consecutive even natural numbers can be expressed as:
- \( x \) (first number)
- \( x + 2 \) (second number)
- \( x + 4 \) (third number)
- \( x + 6 \) (fourth number)
- \( x + 8 \) (fifth number)
- \( x + 10 \) (sixth number)
- \( x + 12 \) (seventh number)

3. **Calculate the Sum of the Numbers**:
The sum of these seven numbers is:
\[ x + (x + 2) + (x + 4) + (x + 6) + (x + 8) + (x + 10) + (x + 12) \]
Simplifying this:
\[ = 7x + (2 + 4 + 6 + 8 + 10 + 12) = 7x + 42 \]

4. **Set Up the Average Equation**:
The average of these numbers is given by the formula:
\[ \text{Average} = \frac{\text{Sum of numbers}}{\text{Total numbers}} = \frac{7x + 42}{7} \]
We know from the problem that the average is 36:
\[ \frac{7x + 42}{7} = 36 \]

5. **Solve for \( x \)**:
To eliminate the fraction, multiply both sides by 7:
\[ 7x + 42 = 252 \]
Now, subtract 42 from both sides:
\[ 7x = 210 \]
Finally, divide by 7:
\[ x = 30 \]

6. **Find the First Number**:
The first number is \( x \), which we found to be 30.

Thus, the value of the first number is **30**.