<PRE><B>Question 979757</B>
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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