Question

The sum of five consecutive integers is five. What is the product of the five integers?

Answer 1

0

Explanation:

If the sum of the integers is 5, then the arithmetic mean of the integers is
`$(5)/(5)=1$` . In five consecutive integers, the arithmetic mean is equal to the middle integer, which means the integers are -1, 0, 1, 2, 3 and the product is
`$\boxed{0}$`.

Hope this helped! :)

Answer 2

The first integer = x

The second integer = x + 1

The third integer = x + 2

The fourth integer = x + 3

The fifth integer = x + 4

Since they all add up to 5, let's set them equal to 5

x + x + 1 + x + 2 + x + 3 + x + 4 = 5

Combine like terms

5x + 10 = 5

Subtract 10 from both sides

5x = -5

Divide each side by 5

x = -1

The first integer = x = -1

The second integer = x + 1 = -1 + 1 = 0

The third integer = x + 2 = -1 + 2 = 1

The fourth integer = x + 3 = -1 + 3 = 2

The fifth integer = x + 4 = -1 + 4 = 3

We can check this by adding all the integers together and making sure we get 5

3 + 2 + 1 + 0 - 1 = 5