The sum of all even numbers between 200 and 500 is 52150.
Here's how to arrive at that answer:
We need to sum the series: 200 + 202 + 204 + ... + 498 + 500. This is an arithmetic progression.
- First term (a): 200
- Last term (l): 500
- Common difference (d): 2
To find the number of terms (n), we use the formula: l = a + (n - 1)d
500 = 200 + (n - 1)2
300 = (n - 1)2
150 = n - 1
n = 151
Therefore, there are 151 terms in the series.
Now, to find the sum (S) of the arithmetic series, we use the formula: S = n/2 * (a + l)
S = 151/2 (200 + 500)
S = 151/2 700
S = 151 * 350
S = 52850
Therefore, the sum of all the even numbers between 200 and 500 is 52850.
