a,b,c,d,e,f,g are consecutive even numbers. J, k, I, m, n are consecutive odd numbers. The average of all the numbers is:

Options

A. `3((a+n)/2)`
B. `(l+d)/2`
C. `(a+b + m +n)/4`
D. `(j + c + n +g)/4`

Answer

To find the average of the consecutive even numbers \( a, b, c, d, e, f, g \) and the consecutive odd numbers \( j, k, l, m, n \), we can follow these steps:

### Step 1: Identify the consecutive even numbers
Let’s denote the first even number as \( a \). The consecutive even numbers can be expressed as:
- \( a \)
- \( a + 2 \)
- \( a + 4 \)
- \( a + 6 \)
- \( a + 8 \)
- \( a + 10 \)
- \( a + 12 \)

### Step 2: Identify the consecutive odd numbers
Let’s denote the first odd number as \( j \). The consecutive odd numbers can be expressed as:
- \( j \)
- \( j + 2 \)
- \( j + 4 \)
- \( j + 6 \)
- \( j + 8 \)

### Step 3: Calculate the average of the even numbers
The average of a set of numbers is calculated by summing the numbers and dividing by the count of the numbers. For the even numbers:
- The middle term (4th number) in the list of 7 consecutive even numbers is \( d = a + 6 \).
- Therefore, the average of the even numbers is \( d = a + 6 \).

### Step 4: Calculate the average of the odd numbers
For the odd numbers:
- The middle term (3rd number) in the list of 5 consecutive odd numbers is \( l = j + 4 \).
- Therefore, the average of the odd numbers is \( l = j + 4 \).

### Step 5: Calculate the overall average
To find the average of all the numbers, we take the average of the averages of the even and odd numbers:
\[ \text{Overall Average} = \frac{(a + 6) + (j + 4)}{2} \]
This simplifies to:
\[ \text{Overall Average} = \frac{(a + j + 10)}{2} \]

### Conclusion
The average of all the numbers \( a, b, c, d, e, f, g, j, k, l, m, n \) is given by:
\[ \text{Overall Average} = \frac{(a + j + 10)}{2} \]