varun289 wrote:The sum of the first 50 positive odd integers is 2,500. What is the sum of the odd integers from 101 to 199, inclusive?
(A) 4,950
(B) 5,000
(C) 7,450
(D) 7,500
(E) 9,950
To calculate the sum of evenly spaced integers:
Sum = (number of integers) * (average of biggest and smallest)
To count the number of evenly spaced integers in a set:
Number of integers = (biggest - smallest)/interval + 1
The INTERVAL is the distance between successive terms.
Since we're adding only the ODD integers here, the interval is 2.
Thus, the number of odd integers from 101 to 199 = (199-101)/2 + 1 = 50.
Average of biggest and smallest = (199+101)/2 = 150.
Sum = (number of integers) * (average of biggest and smallest) = 50*150 = 7500.
The correct answer is
D.
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