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For any positive integer n, the sum of the first n positive integers equals [n(n+1)]/2. What is the sum of all the even integers be tween 99 and 301?
- a)10,100
- b)20,200
- c)22,650
- d)40,200
Correct answer is option 'B'. Can you explain this answer?
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For any positive integer n, the sum of the first n positive integers e...
Sum of the first n positive integers:
The sum of the first n positive integers can be calculated using the formula [n(n+1)]/2. This formula is derived from the concept of arithmetic progression, where the sum of a series of numbers is equal to the average of the first and last term multiplied by the number of terms.
Finding the range of even integers:
To find the sum of all even integers between 99 and 301, we first need to determine the range of even integers within this interval.
The first even integer within this range is 100, and the last even integer is 300. The series of even integers between 100 and 300 can be represented as 100, 102, 104, ..., 298, 300.
Finding the number of even integers:
To find the number of even integers within this range, we can subtract the first even integer from the last even integer and divide by 2.
Number of even integers = (300 - 100)/2 + 1 = 101
Calculating the sum:
Now that we know there are 101 even integers within the range of 99 to 301, we can use the formula for the sum of the first n positive integers to find the sum of these even integers.
Sum = [101(100 + 300)]/2 = 20,200
Therefore, the sum of all the even integers between 99 and 301 is 20,200, which corresponds to option B.
The sum of the first n positive integers can be calculated using the formula [n(n+1)]/2. This formula is derived from the concept of arithmetic progression, where the sum of a series of numbers is equal to the average of the first and last term multiplied by the number of terms.
Finding the range of even integers:
To find the sum of all even integers between 99 and 301, we first need to determine the range of even integers within this interval.
The first even integer within this range is 100, and the last even integer is 300. The series of even integers between 100 and 300 can be represented as 100, 102, 104, ..., 298, 300.
Finding the number of even integers:
To find the number of even integers within this range, we can subtract the first even integer from the last even integer and divide by 2.
Number of even integers = (300 - 100)/2 + 1 = 101
Calculating the sum:
Now that we know there are 101 even integers within the range of 99 to 301, we can use the formula for the sum of the first n positive integers to find the sum of these even integers.
Sum = [101(100 + 300)]/2 = 20,200
Therefore, the sum of all the even integers between 99 and 301 is 20,200, which corresponds to option B.
Community Answer
For any positive integer n, the sum of the first n positive integers e...
70,420
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For any positive integer n, the sum of the first n positive integers equals [n(n+1)]/2. What is the sum of all the even integers be tween 99 and 301?a)10,100b)20,200c)22,650d)40,200Correct answer is option 'B'. Can you explain this answer?
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