Question

Using algebraic methods, prove that the sum of 2 consecutive odd integers is always a multiple of 4.

Answer 1

This statement will always be true practically.

Explanation:

Let the odd number be:

=2x - 1

So the next odd will be:

= 2x + 1

Now for getting sum of two odd numbers we will add them:

= (2x -1)+(2x + 1)

Opening brackets:

= 2x -1 +2x +1

A dding like terms, Both 1's will be cancelled out

= 4x

Now this proves that adding two odd numbers will deduce to a result which will always a multiple of 4

Hence proved.

I hope it will help you!