The sum of the first 60 positive even integers is 3,750.
The sum of the first 60 positive even integers is 3,750. What is the sum of the odd integers from 101 to 200, inclusive?
Answer/Solution
4,700
Steps/Work
101+103+.......199
If we remove 100 from each of these it will be sum of 1st 100 odd numbers.
so 101+103+.......199 = 60 * 100 + (1+3+5+7+......)
sum of 1st 100 natural numbers = (100 * 101) / 2 = 5050
Sum of 1st 60 positive even integers = 3750
sum of 1st 100 odd numbers = 5050 - 3750 = 1300
so 101+103+.......199 = 60 * 100 + (1+3+5+7+......) = 6000 + 1300 =4700
A is the answer.
If we remove 100 from each of these it will be sum of 1st 100 odd numbers.
so 101+103+.......199 = 60 * 100 + (1+3+5+7+......)
sum of 1st 100 natural numbers = (100 * 101) / 2 = 5050
Sum of 1st 60 positive even integers = 3750
sum of 1st 100 odd numbers = 5050 - 3750 = 1300
so 101+103+.......199 = 60 * 100 + (1+3+5+7+......) = 6000 + 1300 =4700
A is the answer.