a, b, c, d, e are five consecutive odd number. Find the average of all this number in terms of a.

Answer

To find the average of five consecutive odd numbers \( a, b, c, d, e \) in terms of \( a \), we can follow these steps:

### Step 1: Define the consecutive odd numbers
Since \( a \) is the first odd number, 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 down the numbers
Now we have the five consecutive odd numbers:
- \( a \)
- \( a + 2 \)
- \( a + 4 \)
- \( a + 6 \)
- \( a + 8 \)

### Step 3: Calculate the sum of these numbers
To find the average, we first need to calculate the sum of these numbers:
\[ \text{Sum} = a + (a + 2) + (a + 4) + (a + 6) + (a + 8) \]
Combining like terms, we get:
\[ \text{Sum} = a + a + a + a + a + 2 + 4 + 6 + 8 = 5a + 20 \]

### Step 4: Calculate the average
The average is calculated by dividing the sum by the total number of observations (which is 5):
\[ \text{Average} = \frac{\text{Sum}}{5} = \frac{5a + 20}{5} \]
Simplifying this gives:
\[ \text{Average} = a + 4 \]

### Final Answer
Thus, the average of the five consecutive odd numbers \( a, b, c, d, e \) in terms of \( a \) is:
\[ \text{Average} = a + 4 \]

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