Numbers and

Question

If the sum of the consecutive integers from -22 to X inclusive is 72. What is the value of X? 

Answer 1

Sarika,

 

I'll attempt to explain.

 

You're asked to find X when:

 

-22 + -21 +... + X = 72

 

Now, adding an integer's opposite to the integer results in 0; for example, -22 + 22 = 0, -21 + 21 = 0, etc.

 

So, if I have this sum:

 

-22 + -21 + -20 +...+20 + 21 + 22, the result is 0, correct?

 

If I now add 23 to this sum, I get:

 

0 + 23 = 23 (not 72)

 

So, let's add 24 to this sum:

 

23 + 24 = 47 (not 72)

 

Add 25 to this sum:

 

47 + 25 = 72 (got it).

 

So, X = 25.

 

The total sum would look like:

 

-22 + -21 + -20 +...+20 + 21 + 22 + 23 + 24 + 25 = 72

 

A bit confusing.

 

Hope this helps.