The sum of the first 25 even counting numbers is 650.
Understanding the concept of even numbers is crucial to solving this problem. Even numbers are integers that are divisible by 2, starting with 2, 4, 6, and so on. To find the sum of the first 25 even numbers, we are looking for the sum of this sequence: 2 + 4 + 6 + ... up to the 50th number (since the 25th even number is 2 * 25 = 50).
There is a simple formula to find this sum. The sum of the first 'n' even numbers is given by n * (n+1). In our case, n is 25. So, the formula becomes 25 * (25 + 1) = 25 * 26 = 650.
Here's a breakdown:
- The first even number is 2.
- The second is 4.
- The third is 6.
- ...and so on.
- The 25th even number is 50.
To confirm this, we can list out some of the numbers and confirm that this formula works:
| First N Even Numbers | Sum | Formula (n*(n+1)) |
|---|---|---|
| 2 | 2 | 1*(1+1) = 2 |
| 2, 4 | 6 | 2*(2+1) = 6 |
| 2, 4, 6 | 12 | 3*(3+1) = 12 |
| 2, 4, 6, 8 | 20 | 4*(4+1) = 20 |
As you can see, the formula holds true for the sum of the first few even counting numbers. Therefore, applying the formula for 25 even numbers also yields the correct sum.
According to the reference provided, the sum of the first 25 even natural numbers is indeed **650**. This confirms our calculations.
