SOLUTION: The sum of 40 consecutive integers is 100. What is the smallest of these 40 integers?

Question 979757: The sum of 40 consecutive integers is 100. What is the smallest of these 40 integers?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
40 consecutive numbers add up to 100.
The numbers have to start less than 1. The average is 2.5, so that is the middle of 40 integers.
sum from -1 to -17 is -{n*(n+1)/2}=-153
numbers 0,1,2 add up to 3.
Integers greater than 2 add up to 250.
Another way of saying that is that we want consecutive numbers from 1 that add up to 253,
n*(n+1)/2=253; n(n+1)=512
n^2+n-506=0; (n+23)(n-22)=0; n=22, -23, positive root only.
The number at the top are 22
The number at the bottom is -17.
Zero is the 40th number.
The consecutive integers (40) are from -17 to 22.
ANSWER: minus 17 is the smallest.

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