Question 1

Let's use algebra to represent any two consecutive odd numbers.

Step 1 — Representing the numbers

We need to pick any odd number. Let's use a variable for this. An odd number can be written as $2n + 1$. Here, $n$ is any whole number. The next consecutive odd number is $2$ more than the first. So, we add 2 to our first number.

$(2n + 1) + 2$

$= 2n + 3$

$\boxed{\text{Second odd number} = 2n + 3}$

Step 2 — Finding their sum

Now, let's add these two consecutive odd numbers. We will sum the first odd number and the second odd number.

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

$= 2n + 1 + 2n + 3$

$= 4n + 4$

We can see that 4 is a common factor here. Let's factor out 4 from the sum.

$= 4(n + 1)$

Since $n$ is a whole number, $n+1$ is also a whole number. This means the sum is 4 multiplied by a whole number. Any number that can be written as 4 times a whole number is divisible by 4.

Answer

The sum of two consecutive odd numbers is divisible by 4.