The sum of all odd whole numbers between 8 and 32 is ______.

Options

A. 240
B. 320
C. 360
D. 260

Answer

To find the sum of all odd whole numbers between 8 and 32, we can follow these steps:

### Step 1: Identify the odd whole numbers between 8 and 32
The first odd whole number greater than 8 is 9, and the last odd whole number less than 32 is 31. The odd whole numbers between 8 and 32 are:
9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31.

### Step 2: Count the number of odd whole numbers
To count the odd numbers, we can list them as follows:
- 9 (1st)
- 11 (2nd)
- 13 (3rd)
- 15 (4th)
- 17 (5th)
- 19 (6th)
- 21 (7th)
- 23 (8th)
- 25 (9th)
- 27 (10th)
- 29 (11th)
- 31 (12th)

There are a total of 12 odd whole numbers between 8 and 32.

### Step 3: Use the formula for the sum of an arithmetic series
The sum \( S_n \) of an arithmetic series can be calculated using the formula:
\[ S_n = \frac{n}{2} \times (a + l) \]
where:
- \( n \) = number of terms
- \( a \) = first term
- \( l \) = last term

In this case:
- \( n = 12 \)
- \( a = 9 \)
- \( l = 31 \)

### Step 4: Substitute the values into the formula
Now we can substitute the values into the formula:
\[ S_{12} = \frac{12}{2} \times (9 + 31) \]
\[ S_{12} = 6 \times 40 \]
\[ S_{12} = 240 \]

### Conclusion
The sum of all odd whole numbers between 8 and 32 is **240**.

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