Final answer:
To find the sum of all the even numbers between 105 and 351, we can use the arithmetic series formula. The sum is 15147.
Step-by-step explanation:
To find the sum of all the even numbers between 105 and 351, we need to identify the even numbers within this range and add them up. We can do this by starting with the first even number, which is 106, and continuously adding 2 until we reach the last even number in the range.
We can calculate the number of terms using the formula ((last term - first term) / common difference) + 1. In this case, the first term is 106, the last term is 350, and the common difference is 2. Therefore, the number of terms is ((350 - 106) / 2) + 1 = 123.
The sum of an arithmetic series can be found using the formula Sn = (n/2)(first term + last term), where Sn is the sum, n is the number of terms, and the first and last terms are given. Plugging in the values, we have Sn = (123/2)(106 + 350) = 15147.
Learn more about finding the sum of even numbers