For any positive integer n, the sum of first n positive integer equals n(n+1)/2. What is the sum of all the even integers between 99 and 301?
A) 10,100
B) 20,200
C) 22,650
D) 40,200
E) 45,150
The question asks for the sum of the even integers from 100 to 300, inclusive.
Ignore the formula given. Instead, the following can be used to calculate the sum of any set 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 one term and the next.
Since we're adding only the even integers here, the interval is 2.
Thus, the number of even integers from 100 to 300 = (300-100)/2 + 1 = 101.
Average of biggest and smallest = (300+100)/2 = 200.
Sum = (number of integers) * (average of biggest and smallest) = 101*200 = 20,200.
The correct answer is
B.
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