can someone explain this?

Question

Question
The sum of any 4 consecutive numbers is even. explain how this is true.

Answer 1

Let's prove it algebraically. (I'm assuming these are integers.)

Let n = first number
n+1 = 2nd number
n+2 = 3rd number
n+3 = 4th number

Their sum is n + (n+1) + (n+2) + (n+3)

Rearranging: n + n + n + n + 1 + 2 + 3

Simplifying: 4n + 6

When you multiply *any* integer by an even number, the product is even. So 4n is always going to be an even number.

Adding an even number, 6, to a term that is always even, 4n, will result in an even number.

Therefore, the sum of any 4 consecutive numbers (integers) is even.

Answer 2

Well 2+3+4+5=14

Answer 3

Let the first number of the consecutive sequence be a.
Therefore, the 2nd number is a + 1, the 3rd number is a + 2 and the 4th number is a + 3.

The sum of 4 consecutive numbers :
a + (a + 1) + (a + 2) + (a + 3) = 4a + 6
4a + 6 is divisible by 2 ---> (4a + 6) / 2 = 2a + 3.

To check :
Let the 4 consecutive numbers be 1,2,3 and 4.
1 + 2 + 3 + 4 = 10
10 / 2 = 5

I hope this has helped you.

Answer 4

a a+1 a+2 and a+3 it will be any 4 consecutive numbers put them together (sorry for my English) it will be:a+a+1+a+2+a+3=4a+6=2(a+3) does not matter what you put for "a" you can always divide 2(a+3) on 2 which means sum will be even

Answer 5

The sum of any two odd numers is always a even number
ex)1+3=4
37+49=86
9+11=20
When we have 4 consecutive numers there are alwys two even and two odd numbers

Two odd numbers when added together always equal an even number

It follows whenevr two even numbers are added together the result is always even

so the resut is the sum of any 4 consecutive numbers is even.

Answer 6

start by looking at the sum of two numbers. I'll use E to denote even and O to denote odd numbers.

E + E = E
O + E = O
O + O = E

Think about the odds have having an extra 1. so if you add a odd and and odd the two extra 1's sum to a 2 and you now have a even sum.

for four consecutive numbers you will have one of two set ups...

E O E O or O E O E

E + O = O so for each of the two set ups you will end up with

O + O = E

Hope that helps.

Answer 7

When you add 4 consecutive numbers we know we will be adding 2 odds and 2 evens.

Break it up into 2 pieces.
Even + Even = Even
Odd + Odd= Even

Therefore we have Even+Even= Even!

So no matter which numbers they are they will always make a n even number, because we know there will always be 2 evens and 2 odds to make another even :)

Hope this helps

Answer 8

So many people would accept that the sum of any 4 consecutive numbers is even and never question it.

Good for you for asking this question.

I wonder if it should be 4 consecutive integers ?

Answer 9

consider the numbers n,n+1,n+2 and n+3. their sum is 4n+6=2(n+3) which is even

Answer 10

Let numbers be n , n + 1 , n + 2 , n + 3
Sum = 4n + 6
Sum = 2(2n + 3)
Let 2n + 3 = k
Sum = 2k
2k is an EVEN number for all integer k