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# Which 2 consecutive integers have a sum of -105

Which 2 consecutive integers have a sum of -105

### 3 Answers by Expert Tutors

Ralph K. | Effective Mathematics, Physics and Chemistry TutorEffective Mathematics, Physics and Chemi...
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Do not be bothered by the fact that the sum of the two consecutive integers is negative, as the means of answering the problem is identical for both positive and negative answers.  Allen above gave the algebraic solution to the problem so I will simply describe a method of thinking about the problem logically and working it out without covering it to an equation.

First any two consecutive integers add up to an odd number.  This is by definition because with two consecutive integers one will be positive and one will be negative thus when added together it always produces a negative result.

For example 1,2 give 3 (1+2=3) and 2,3 give 5 (2+3=5).

If you subtract 1 from the sum and divide by 2 you will get the first number in the sequence because as Allen said the equation is n + (n+1) = -105.  By subtracting 1 from the sum.  In this case -105 - 1 gives = -106.  diving by 2 give -53.

Thus the answer is -53 and -52.  If the sum had been positive 105 you would subtract 1 and get 104, half of which is 52. Thus the answer would be 52, and 53.  As I said it really does make any difference if you are working with positive numbers or negative numbers the answer is the same except for the sign.

-105 yields consecutive integers of -53 and -52 .
105 yields consecutive integers of   52 and  53 .

-1 would yield consecutive integers of -1 and 0 .
1 would yield consecutive integers of  0 and 1 .
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Brad, I hope you have an understanding of negative numbers.  If I asked you to find the same for 105, how would you do it?  The numbers have to be close to each other, which means they'd probably start at around half of -105.

What's half of -105?  Half of -100 is -50. Half of -5 is -2 1/2.  -52 1/2 is not an integer, but your two integers lie on either side.

-52 + -53 = -105

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Allen B. | Experienced tutor of Algebra, Precalculus, Calculus and PhysicsExperienced tutor of Algebra, Precalculu...
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let n= one of the integers (the lesser one)
then since they are consecutive, the other is (n+1).
Now just write the problem as an equation:

n + (n+1) = -105

can you solve it?