Question

The sum of three consecutive odd numbers is -27. What is the largest of the three numbers

Answer 1

1. Some "odd" logic (...sorry)

An odd number can be written as $2n+1$ where n is an integer.

If $2n+1$ is our first odd number, the next consecutive odd number will be 2 more than that. The third one will be 4 more.

If we only add 1, we'd get an even number, so we need to add 2.

2. What are the expressions for our numbers?

First number:

$2n+1$

Second number (2 more than the first number):

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

Third number (4 more than the first number):

$2n+1+4 = 2n+5$

3. Adding our numbers together

The sum is these 3 numbers added together. Let's do that now:

$(2n+1) + (2n+3) + (2n+5)$

$2n + 2n + 2n + 1 + 3 + 5\\6n + 9$

4. Solving the equation

The sum is, thus, $6n+9$. We know this sum is equal to -27:

$6n+9 = -27$

Subtract 9 from both sides:

$6n = -36$

Divide both sides by 6:

$n = -6$

5. Finding our numbers

Now that we know n, we can find our 3 numbers.

For the first number, we can use its expression in section 2.

$2n +1 = 2*(-6)+1 = -12+1 = -11$

For the second number, we can just use the fact that it's 2 more than our first number, -11. If you're wondering why this is, review section 1.

$-11 + 2 = -9$

Same for our third number, it's 4 more than our first number or 2 more than our 2nd number:

$-11 + 4 = -7\\or\\-9 + 2 = -7$

6. So the largest one is...?

Our three consecutive numbers are -11, -9, and -7. As we can see, the largest of these three is -7.

Answer: -7