Question

Prove or disprove , the sum of any four consecutive integers is even.

Answer 1

The sum of any four consecutive integers can be algebraically expressed and simplified to show that it is always even, proving the statement correct.

Step-by-step explanation:

To prove or disprove that the sum of any four consecutive integers is even, we can represent the four consecutive integers algebraically. Let the first integer be n. The next three consecutive integers would be n+1, n+2, and n+3. The sum of these four integers is:

n + (n+1) + (n+2) + (n+3)

Combine like terms:

4n + 6

Now, we can factor out the common factor of 2:

2(2n + 3)

Since the number being multiplied by 2 (which is even) is an integer, the overall sum must also be even. This demonstrates that the sum of any four consecutive integers is, indeed, always even. Therefore, we have proved the statement.