# Math Help - Consecutive integer question

1. ## Consecutive integer question

How would I go about solving this question?

The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are there in this set?

I have no idea how to solve this question. I guess I would start off with
-25 + -24 + -23 + -22 + -21, and continue but that would be impracticle, is there any way to use algebra or something to solve this type of question? Please help! Thankyou.

2. Originally Posted by gs.sh11
How would I go about solving this question?

The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are there in this set?

I have no idea how to solve this question. I guess I would start off with
-25 + -24 + -23 + -22 + -21, and continue but that would be impracticle, is there any way to use algebra or something to solve this type of question? Please help! Thankyou.
Well..

$-25 -24 -23 - ... -1 + 0 + 1 + ... +23 + 24 + 25 = 0$ so obviously the last number would be 26

Now, I assume you know how many numbers there are in $\left\{-25,-24,...,-1,0,1,...,24,25,26\right\}$

3. Originally Posted by gs.sh11
How would I go about solving this question?

The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are there in this set?

I have no idea how to solve this question. I guess I would start off with
-25 + -24 + -23 + -22 + -21, and continue but that would be impracticle, is there any way to use algebra or something to solve this type of question? Please help! Thankyou.
Well think about it. In order to get to 0, you must have ALL the positive numbers the same as all the negative numbers. In other words, if you start with -25, and you want to get 0, then your sum will have to include at least up to 25. -24 will cancel with 24, -23 will cancel with 23.

So in other words, if you go:

-25 - 24 -23....+23 + 24 +25, you are at zero. So all the numbers form there onwards have to sum to 26. And the next number in the series, as it happens, is 26.

So your sum has ALL the integers from -25 to 26.