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Sum of First 50 Odd Numbers
Difficulty Level     In a classroom, a Maths teacher is asking questions to her students. She first asked the class to see if they could find the sum of the first 50 odd numbers. As everyone settled down to their addition, Mark ran to her and said, The sum is 2,500. The teacher was surprised so to test if Mark actually calculated the sum or was guessing she gave him the task of finding the sum of the first 75 odd numbers.Within 20 seconds, Mark was back with the correct answer.
How does Mark find the sum so quickly and what is the answer

Sum of first 50 odd numbers
The first 50 odd number series will start from 1,3,5... and the highest is 99.
Mark made the odd numbers as pairs like
(1,99)
(3,97)
(5,95)
....
....
(47,53)
(49,51)
Sum of each pair is 100 and there are 25 pairs.

So total sum will be 25 x 100 = 2500

Now lets take the case of first 75 odd numbers

Pair the odd numbers as
(1,149)
(3,147)
(5,145)
(7,143)
(9,141)
......
......
......
(69,81)
(71,79)
(73,77)
(75)
There are 37 such pairs and 75 left at the last which doesnt contain any pair
Sum of numbers in each pair is 150

So total sum will be (150 X 37) + 75 = 5625

By Calculating this way, Mark answered the questions so fast.