# Find three consecutive numbers that add up to these numbers

• Sep 23rd 2009, 09:40 AM
Julian.Ignacio
Find three consecutive numbers that add up to these numbers
for example: 141+142+143 add up to 426

Now what I need to do is explain the procedure (how did I get this kind of answer etc.). Sorry I really don't know how to find the formula..

4 consecutive, even numbers that add up to 1172
5 ~ that add up to 1172
• Sep 23rd 2009, 09:55 AM
masters
Quote:

Originally Posted by Julian.Ignacio
for example: 141+142+143 add up to 426

Now what I need to do is explain the procedure (how did I get this kind of answer etc.). Sorry I really don't know how to find the formula..

4 consecutive, even numbers that add up to 1172
5 ~ that add up to 1172

Hi Julian,

Consecutive integers can be defined as x, x + 1, x + 2, x + 3, etc., where x is an integer.

Consecutive even integers can be defined as x, x + 2, x + 4, x + 6, etc., where x is an even integer.

Let x = 1st even number

Let x + 2 = 2nd even number

Let x + 4 = 3rd even number

Let x + 6 = 4th even number

Now add them to obtain the desired sum.

x + x + 2 + x + 4 + x + 6 = 1172

Solve for x, and then determine the 2nd, 3rd and 4th even numbers.

The second part of your question is vague. There are no 5 consecutive even integers that add up to 1172.

x + x + 2 + x + 4 + x + 6 + x + 8 =1172

In the above equation, x is not an integer.
• Sep 23rd 2009, 10:25 AM
Julian.Ignacio
YOu're right, the last one IS impossible...is putting parentheses useless in this calculation? And why?
• Sep 23rd 2009, 12:04 PM
e^(i*pi)
The additive identity does not require them. Mathematically:

$a+(b+c) = (a+b)+c = b+(a+c) = a+b+c$

You can still put them in if you wish to make the working clearer though