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.