The sum of the first even numbers up to and including 100 is 2550.
Explanation:
Even numbers are integers divisible by 2. The even numbers up to 100 are: 2, 4, 6, 8, ..., 100. This forms an arithmetic sequence where:
- The first term (a) = 2
- The common difference (d) = 2
- The last term (l) = 100
To find the sum of this arithmetic sequence, we first need to determine the number of terms (n). Since each term is 2 more than the previous, and they are all even, we can find 'n' by dividing the last term by the common difference divided by two:
n = 100 / 2 = 50
Therefore, there are 50 even numbers from 2 to 100.
Now, we can use the formula for the sum of an arithmetic series:
S = (n/2) * (a + l)
Where:
- S = the sum of the series
- n = the number of terms
- a = the first term
- l = the last term
Plugging in the values:
S = (50/2) (2 + 100)
S = 25 102
S = 2550
Therefore, the sum of the first even numbers up to 100 is 2550.
