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What is the sum of the even integers between 200 and 400, inclusive?
- a)29,700
- b)30,000
- c)30,300
- d)60,000
- e)60,300
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
What is the sum of the even integers between 200 and 400, inclusive?a)...
To find the sum of the even integers between 200 and 400, inclusive, we need to determine the first even number within this range and the last even number within this range, and then calculate the sum.
The first even number within the range is 200, and the last even number within the range is 400. We can calculate the number of even numbers within this range by subtracting the first even number from the last even number and adding 2 (since both 200 and 400 are inclusive).
Number of even numbers = (400 - 200) / 2 + 1 = 101
To find the sum of the even numbers, we can use the formula for the sum of an arithmetic series:
Sum = (n/2)(first term + last term)
where n is the number of terms.
Sum = (101/2)(200 + 400) = 50.5(600) = 30,300
Therefore, the sum of the even integers between 200 and 400, inclusive, is 30,300. Thus, the correct answer is option C.
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Community Answer
What is the sum of the even integers between 200 and 400, inclusive?a)...
Sum of Even Integers between 200 and 400, inclusive
To find the sum of even integers between 200 and 400, we need to first identify the even integers in this range and then calculate their sum.
Identifying Even Integers
Even integers are those integers that are evenly divisible by 2. In this case, we need to find even integers between 200 and 400, inclusive.
First, let's find the smallest even integer in the range. Since 200 is divisible by 2, it is an even integer.
Next, let's find the largest even integer in the range. Since 400 is also divisible by 2, it is an even integer.
Calculating the Sum
To calculate the sum of a sequence of numbers, we can use the formula for the sum of an arithmetic series. The formula is:
Sum = (n/2)(first term + last term)
Here, n represents the number of terms in the sequence. In this case, the number of even integers between 200 and 400 is (400 - 200)/2 + 1 = 101.
The first term is 200 and the last term is 400.
Plugging these values into the formula, we get:
Sum = (101/2)(200 + 400) = 50.5 * 600 = 30,300
Conclusion
Therefore, the sum of the even integers between 200 and 400, inclusive, is 30,300. Hence, the correct answer is option 'C'.
To find the sum of even integers between 200 and 400, we need to first identify the even integers in this range and then calculate their sum.
Identifying Even Integers
Even integers are those integers that are evenly divisible by 2. In this case, we need to find even integers between 200 and 400, inclusive.
First, let's find the smallest even integer in the range. Since 200 is divisible by 2, it is an even integer.
Next, let's find the largest even integer in the range. Since 400 is also divisible by 2, it is an even integer.
Calculating the Sum
To calculate the sum of a sequence of numbers, we can use the formula for the sum of an arithmetic series. The formula is:
Sum = (n/2)(first term + last term)
Here, n represents the number of terms in the sequence. In this case, the number of even integers between 200 and 400 is (400 - 200)/2 + 1 = 101.
The first term is 200 and the last term is 400.
Plugging these values into the formula, we get:
Sum = (101/2)(200 + 400) = 50.5 * 600 = 30,300
Conclusion
Therefore, the sum of the even integers between 200 and 400, inclusive, is 30,300. Hence, the correct answer is option 'C'.
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