Help on math question??!!?

Question

If the sum of the consecutive integers from -22 to x, inclusive is 72, what is the valueof x?

Apparently the answer is 25. However, that doesn't make any sense to me. IF xis 25, then wouldn't the sum be 3?

Answer 1

adding consecutive integers will never make a even number

Answer 2

The numbers are concecutive (one after the other) with the starting number being -22.

Think of the Integer number line. Zero is in the middle, with negative numbers to the left and positive numbers to the right

<-------------------------------------...

...-100          -50                   0                      50            100......

Hence, if you consider the sum of concecutive number from left to right, starting with -22, it will be like this...

-22+ -21 + -20 + .....0 +1+2+3+4+....22... and so on.

When we reach 22, then the sum will be zero, because the posetive numbers will cancel out the negative numbers. (-21 with 21 and so on).

So, not, we just have to add concecutive numbers from 23 to reach 72.  This will be 23+34+25 = 72.

Hence, X is 25 (the last number in the series, inclusive).

This is the less mathematical but more intuitive version it. You can also solve this by using Algebra and equations, but this way is more fun.

Answer 3

it is 25