Consecutive Numbers and Their Properties

This video tutorial explores algebraic proofs, demonstrating how to prove various mathematical statements using algebra. It covers proving that the sum of three consecutive integers is a multiple of three, the sum of two consecutive integers is always odd, and the sum of two consecutive odd numbers is a multiple of four. Additionally, it shows that the product of two even numbers is a multiple of four, the difference between the squares of two consecutive odd numbers is a multiple of eight, and the difference between the squares of two consecutive integers equals their sum. The video concludes with proving that the sum of the squares of two consecutive even numbers is a multiple of four and the difference of squares of three n's is a multiple of twelve.

What does it mean for numbers to be consecutive?

• They are all odd.

• They are in a sequence without gaps.

• They are all prime numbers.

• They are all even.

If n is a number, what are the next two consecutive numbers?

• n+1 and n+2

• n+2 and n+3

• n+1 and n+3

• n+2 and n+4

Why is the sum of three consecutive integers always a multiple of three?

• Because they are all odd.

• Because they can be expressed as 3 times a number.

• Because they are all even.

• Because they are all prime.

What is the sum of two consecutive integers n and n+1?

• 2n

• 2n+1

• n+1

• n

Why is the sum of two consecutive integers always odd?

• Because one is even and the other is odd.

• Because both are even.

• Because both are odd.

• Because they are both prime.

What is the sum of two consecutive odd numbers?

• 4n+1

• 4n+4

• 4n+2

• 4n

Why is the sum of two consecutive odd numbers always a multiple of four?

• Because they are both even.

• Because they can be expressed as 4 times a number.

• Because they are both odd.

• Because they are both prime.

What is the product of two even numbers 2n and 2m?

• 2nm

• 4nm

• 8nm

• nm

Why is the product of two even numbers always a multiple of four?

• Because they are both odd.

• Because they are both even.

• Because they can be expressed as 4 times a number.

• Because they are both prime.

What is the difference between the squares of two consecutive odd numbers?

• 8n

• 8n+8

• 8n+2

• 8n+4