The sum of all even numbers from 1 to 50 can be found using the formula for the sum of an arithmetic sequence:

\[
S_n = \frac{n}{2} \times (a + l)
\]

Where:
- \(S_n\) is the sum of the arithmetic sequence.
- \(n\) is the number of terms.
- \(a\) is the first term.
- \(l\) is the last term.

In this case:
- The even numbers between 1 and 50 form an arithmetic sequence: \(2, 4, 6, \dots, 50\).
- The first term \(a = 2\).
- The last term \(l = 50\).
- The common difference between terms is \(2\).

To find \(n\), the number of terms:
\[
n = \frac{50 - 2}{2} + 1 = 25
\]

Now, using the formula:
\[
S_{25} = \frac{25}{2} \times (2 + 50) = \frac{25}{2} \times 52 = 25 \times 26 = 650
\]

So, the sum of all even numbers from 1 to 50 is **650**.

Would you like further details or have any questions?

Here are some related questions for you:
1. How do you calculate the sum of odd numbers from 1 to 50?
2. What is the sum of all multiples of 5 from 1 to 100?
3. How can you find the sum of the first 100 even numbers?
4. How would you calculate the sum of squares of even numbers from 1 to 50?
5. What is the sum of all prime numbers from 1 to 50?

**Tip:** Arithmetic sequences are often used to simplify summation problems when the numbers follow a regular pattern.

Learn how to calculate the sum of all even numbers from 1 to 50 using the arithmetic sequence formula. The solution covers key math concepts such as arithmetic progression, summation, and even number patterns, ideal for students in Grades 6-8. The total sum is 650.

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