Question 488075: The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are in this set?
Answer by Jstrasner(112)   (Show Source):
You can put this solution on YOUR website! Hey,
So for this problem we need to look at what we know:
First, the numbers in this set are consecutive, which means that there is a difference of 1 between them. For example 1,2,3,4,5.....
Second, the sum of the integers in this set is a positive number (26), so we need to find a way to cancel out the negative numbers from -25 to 0.
If we wanted to cancel out the negative power of -4 for instance, we would add 4 to it. That way the sum would be (-4) + (-3) + (-2) + (-1) + 1 + 2 + 3 + 4 = 0 .
So for this problem, if we add all of the numbers from -25 to +25, the end result would be 0. Then the next number after +25 is +26, which is the sum. Therefore,
the number of integers in this set include the first 25 negative numbers, the second 25 positive numbers and the 26 (which comes after positive 25). Therefore, the total number of integers is:
25 + 25 + 1 = 51.
I know it's a little confusing. Just look over the problem a few times and this solution and you'll get it.
I hope this helps!
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