What is the sum of all odds intergers between 8 and 26 with solution 

To find the sum of all odd integers between 8 and 26, let's follow these steps:

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

### Step 2: Use the formula for the sum of an arithmetic sequence.
The odd integers form an arithmetic sequence where the first term \(a = 9\), the common difference \(d = 2\), and the last term \(l = 25\).

The sum \(S_n\) of an arithmetic sequence is given by the formula:
\[
S_n = \frac{n}{2} \times (a + l)
\]
where:
- \(n\) is the number of terms,
- \(a\) is the first term,
- \(l\) is the last term.

### Step 3: Determine the number of terms \(n\).
To find \(n\), we use the formula for the \(n\)-th term of an arithmetic sequence:
\[
l = a + (n-1) \times d
\]
Substituting the values, we get:
\[
25 = 9 + (n-1) \times 2
\]
Solving for \(n\):
\[
25 - 9 = (n-1) \times 2
\]
\[
16 = (n-1) \times 2
\]
\[
n-1 = 8 \quad \Rightarrow \quad n = 9
\]

### Step 4: Calculate the sum.
Now that we know \(n = 9\), \(a = 9\), and \(l = 25\), we can calculate the sum:
\[
S_n = \frac{9}{2} \times (9 + 25) = \frac{9}{2} \times 34 = 9 \times 17 = 153
\]

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

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Do you want further details or have any questions?

Here are 5 related questions:
1. What is the sum of all even integers between 10 and 30?
2. How do you find the sum of integers in a geometric sequence?
3. What is the sum of all integers between 1 and 100?
4. Can you generalize the formula to find the sum of odd integers in any given range?
5. How does the sum of an arithmetic series differ from the sum of a geometric series?

**Tip**: To quickly find the number of terms in an arithmetic sequence, use the formula for the \(n\)-th term!

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

Find the sum of all odd integers between 8 and 26 using arithmetic sequence formulas. This math problem explores key concepts such as arithmetic sequences and the sum of sequences. Suitable for students in Grades 6-8.

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