What is the sum of all the odd integers between 8 and 26?

To find the sum of all the odd integers between 8 and 26, we can follow these steps:

### Step 1: Identify the odd integers in the range
The odd integers between 8 and 26 are:  
9, 11, 13, 15, 17, 19, 21, 23, 25.

### Step 2: Count the number of odd integers
There are 9 odd integers in this range.

### Step 3: Calculate the sum using the formula for the sum of an arithmetic series
The sum \( S \) of an arithmetic series can be calculated using the formula:
\[
S = \frac{n}{2} \times (a_1 + a_n)
\]
where:
- \( n \) is the number of terms,
- \( a_1 \) is the first term,
- \( a_n \) is the last term.

For our series:
- \( n = 9 \) (number of terms),
- \( a_1 = 9 \) (first term),
- \( a_n = 25 \) (last term).

Substituting into the formula:
\[
S = \frac{9}{2} \times (9 + 25) = 4.5 \times 34 = 153
\]

### Conclusion:
The sum of all the odd integers between 8 and 26 is \( \boxed{153} \).

Would you like more details or have any questions?

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Here are some related questions:
1. What is the sum of all even integers between 8 and 26?
2. How many odd integers are there between 10 and 30?
3. What is the sum of all odd integers between 1 and 100?
4. How would you calculate the sum of all even integers between 1 and 50?
5. What is the arithmetic mean of the odd integers between 8 and 26?
6. Can you find the sum of all multiples of 3 between 8 and 26?
7. What is the general formula for the sum of the first \( n \) odd numbers?
8. How would the sum change if the range was from 9 to 27?

**Tip:** Arithmetic series formulas are handy for quickly summing sequences with a constant difference.

Learn how to find the sum of all odd integers between 8 and 26 step-by-step. This problem involves identifying odd numbers, applying the formula for the sum of an arithmetic series, and basic arithmetic calculations. Suitable for students in Grades 6-8.

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