Myriora Maths › 11+ maths › Chapter 2: Classic word problems

Consecutive numbers

11+Chapter 2 · Lesson 4

In this lesson

Consecutive numbers come one after another.
An odd number of them adds up to how many there are, times the middle number.
With an even number, the middle is halfway between two numbers.
Divide to find the middle, then step out on each side.

Your turn

Three numbers in a row have a total of seventy-two. What is the biggest one?

Show the answer

Seventy-two divided by three is twenty-four: that's the middle number. So the numbers are twenty-three, twenty-four and twenty-five. The biggest is twenty-five!

The common mistake

A common mistake is dividing, and stopping there. Thirty-five is just the middle number. The question asks for all three numbers: thirty-four, thirty-five and thirty-six.

Try it at home

Add three page numbers in a row in any book. Is the total always three times the middle page?

Read the whole lesson

Hello, and welcome to Myriora Maths! Three numbers in a row have a total of one hundred and five. What are they? There's a neat trick: look at the middle one.

First, what are numbers in a row? They're called consecutive numbers, like twelve, thirteen and fourteen. Each one is one more than the one before.

Here's the trick. The first number is one less than the middle. The last number is one more than the middle. So if we move one from the last number to the first, all three become the middle number! So the total of three numbers in a row is three times the middle number.

So, three times the middle number is one hundred and five. The middle number is one hundred and five divided by three: thirty-five. So the numbers are thirty-four, thirty-five and thirty-six!

It works for more numbers too, as long as there's a middle one. The total of five numbers in a row is five times the middle number. If five numbers in a row have a total of sixty, the middle one is twelve. So they're ten, eleven, twelve, thirteen and fourteen.

What about an even number of them, like four numbers in a row with a total of fifty? There's no middle number now, so the middle sits halfway between two numbers. Fifty divided by four is twelve and a half. That's halfway between twelve and thirteen. So the numbers are eleven, twelve, thirteen and fourteen!

A common mistake is dividing, and stopping there. Thirty-five is just the middle number. The question asks for all three numbers: thirty-four, thirty-five and thirty-six.

Your turn! Three numbers in a row have a total of seventy-two. What is the biggest one? You've got twenty seconds, or pause the video if you need more time. Go!

Time's up! Seventy-two divided by three is twenty-four: that's the middle number. So the numbers are twenty-three, twenty-four and twenty-five. The biggest is twenty-five!

Quick review. Consecutive numbers come one after another. An odd number of them adds up to how many there are, times the middle number. With an even number, the middle is halfway between two numbers. Divide to find the middle, then step out on each side. See you next time!