SOLUTION: The least integer of a set of consecutive integers is minus 25. If the sum of these integers is 26, how many integers are in this set? Thanks.

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: The least integer of a set of consecutive integers is minus 25. If the sum of these integers is 26, how many integers are in this set? Thanks.      Log On


   

Question 349208: The least integer of a set of consecutive integers is minus 25. If the sum of these integers is 26, how many integers are in this set?
Thanks.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
In order for the sum of all these integers to be a positive 26 we must have enough positive integers to cancel out all the negative integers plus enough other positive integers to add up to 26. With a like thought we will realize that
1 will cancel out -1
2 will cancel out -2
3 will cancel out -3
etc.
25 will cancel out -25
So the consecutive integers from -25 to 25 will add up to zero! The next integer, 26, will bring the grand total up to 26!

So to get a sum of 26 we have
-25 to -1: 25 integers
1 to 26: 26 integers
and don't forget 0: 1 integer.
This makes a total of 52 consecutive integers from -25 to 26.