The average of any 5 cosecutive odd numbers a,b,c,d and e is:

Options

A. (abcde)/5
B. bd//3
C. ((a+c+e)/5)
D. none of these

Answer

To find the average of any 5 consecutive odd numbers \( a, b, c, d, \) and \( e \), we can follow these steps:

### Step 1: Define the 5 consecutive odd numbers
Let the first odd number be \( a \). The next four consecutive odd numbers can be expressed as:
- \( b = a + 2 \)
- \( c = a + 4 \)
- \( d = a + 6 \)
- \( e = a + 8 \)

### Step 2: Write the sum of these numbers
Now, we can find the sum of these 5 numbers:
\[ \text{Sum} = a + b + c + d + e \]
Substituting the values of \( b, c, d, \) and \( e \):
\[ \text{Sum} = a + (a + 2) + (a + 4) + (a + 6) + (a + 8) \]
\[ \text{Sum} = a + a + 2 + a + 4 + a + 6 + a + 8 \]
\[ \text{Sum} = 5a + (2 + 4 + 6 + 8) \]
Calculating the constants:
\[ 2 + 4 + 6 + 8 = 20 \]
So, the sum becomes:
\[ \text{Sum} = 5a + 20 \]

### Step 3: Calculate the average
The average of these 5 numbers is given by the formula:
\[ \text{Average} = \frac{\text{Sum}}{5} \]
Substituting the sum we found:
\[ \text{Average} = \frac{5a + 20}{5} \]
Breaking it down:
\[ \text{Average} = \frac{5a}{5} + \frac{20}{5} \]
\[ \text{Average} = a + 4 \]

### Step 4: Conclusion
Thus, the average of any 5 consecutive odd numbers \( a, b, c, d, \) and \( e \) is:
\[ \text{Average} = a + 4 \]
Since \( c \) is the middle number in the sequence of 5 consecutive odd numbers, we can also say:
\[ \text{Average} = c \]