The sum of the first 50 positive even integers is 2550. What is the sum of even integers from 102 to 200 inclusive?

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The sum of the first 50 positive even integers is 2550. What is the sum of even integers from 102 to 200 inclusive?

A. 5,100
B. 7,550
C. 10,100
D. 15,500
E. 20,100

The OA is B

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BTGmoderatorLU wrote:
Thu Jan 21, 2021 2:27 pm
The sum of the first 50 positive even integers is 2550. What is the sum of even integers from 102 to 200 inclusive?

A. 5,100
B. 7,550
C. 10,100
D. 15,500
E. 20,100
For any evenly spaced set:
Count = (biggest - smallest)/increment + 1
Average = (biggest + smallest)/2
Sum = (count)(average)

In the problem above:
Smallest = 102
Biggest = 200
Increment = 2 (the distance between one even integer and the next)

Thus:
Count = (200-102)/2 + 1 = 50
Average = (200+102)/2 = 151
Sum = 50*151 = 7550

The correct answer is B.
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