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.