Step by step
The question
Question: prove that the sum of five consecutive integers is a multiple of 5.
1 Write it with letters
Call the first number n, a whole number.
The next integers are 1 more each time: n + 1, n + 2, n + 3, n + 4.
Careful!
An example shows one number.
The letters show every number at once.
2 Put them in
Add them up.
3 Work it out
Open the brackets: n + n + 1 + n + 2 + n + 3 + n + 4.
Like terms together: 5n + 10.
4 Show the form
Every term has a 5 in it.
We take out 5: 5(n + 2).
n + 2 is a whole number, because whole numbers added and multiplied stay whole.
5 times a whole number: so the sum is a multiple of 5.
The square at the end means: the proof is done.
5 Check
An example: 3, 4, 5, 6, 7.
It gives 25.
25 is 5 times 5: a multiple of 5, as the proof says.
Right!
Let's look back.
First: write it with letters.
Then: put them in.
Then: work it out.
Then: show the form.
Last: check.