`a_(1),a_(2),a_(3),a_(4)` & `a_(5)` are five consecutive odd integers, then their mean is.

Options

A. `a_(1)+4`
B. `5(a_(1)+a_(2)+ --+a_(5))`
C. `(a_(1)xxa_(2)xxa_(3)xxa_(4)xxa_(5))/(5)`
D. `A_(1)+5`

Answer

To find the mean of five consecutive odd integers, we can follow these steps:

### Step 1: Define the first odd integer
Let the first odd integer be \( a_1 \).

### Step 2: Express the consecutive odd integers
The next four consecutive odd integers can be expressed as:
- \( a_2 = a_1 + 2 \)
- \( a_3 = a_1 + 4 \)
- \( a_4 = a_1 + 6 \)
- \( a_5 = a_1 + 8 \)

### Step 3: Write the sum of these integers
Now, we can find the sum of these five integers:
\[ \text{Sum} = a_1 + a_2 + a_3 + a_4 + a_5 \]
Substituting the values from Step 2:
\[ \text{Sum} = a_1 + (a_1 + 2) + (a_1 + 4) + (a_1 + 6) + (a_1 + 8) \]

### Step 4: Simplify the sum
Combining like terms:
\[ \text{Sum} = a_1 + a_1 + 2 + a_1 + 4 + a_1 + 6 + a_1 + 8 \]
\[ \text{Sum} = 5a_1 + (2 + 4 + 6 + 8) \]
Calculating the constant sum:
\[ 2 + 4 + 6 + 8 = 20 \]
Thus, the total sum becomes:
\[ \text{Sum} = 5a_1 + 20 \]

### Step 5: Calculate the mean
The mean is calculated by dividing the sum by the number of integers:
\[ \text{Mean} = \frac{\text{Sum}}{5} = \frac{5a_1 + 20}{5} \]
This simplifies to:
\[ \text{Mean} = a_1 + 4 \]

### Conclusion
The mean of five consecutive odd integers \( a_1, a_2, a_3, a_4, a_5 \) is \( a_1 + 4 \).

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