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Consecutive Numbers

Find the consective numbers that are added or multiplied to give the given totals.

Level 1 Level 2 Exam-Style Description Help More Algebra

Consecutive Numbers are numbers which follow each other in order; for example 7,8,9,10. For this exercise all answers are positive numbers.

Three consecutive numbers added together give the answer eighteen. What is the smallest of those numbers?18

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Three consecutive numbers added together give the answer thirty six. What is the smallest of those numbers?36

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Three consecutive numbers added together give the answer sixty three. What is the smallest of those numbers?63

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Five consecutive numbers added together give the answer one hundred and eighty. What is the smallest of those numbers?180

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Five consecutive numbers added together give the answer two hundred and sixty five. What is the smallest of those numbers?265

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The largest of five consecutive numbers is one hundred and sixteen. What is the smallest of those numbers?116

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The largest of five consecutive numbers is twenty six. What is the sum of those numbers?26

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The largest of ten consecutive numbers is twenty three. What is the sum of those numbers?23

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Seven consecutive even numbers add up to one hundred and twelve. What is the smallest of those numbers?112

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Four consecutive odd numbers have a mean of seventeen. What is the smallest of those numbers?17

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Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

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Description of Levels

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Level 1 - Questions about the addition of consecutive numbers

Level 2 - Questions about the multiplication of consecutive numbers

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

More on this topic including lesson Starters, visual aids and investigations.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Example 1

Three consecutive numbers added together give the answer thirty three. What is the smallest of those numbers?

Let the smallest number be x.

The other two numbers can be written as x+1 and x+2.

The sum of the three numbers is x + x+1 + x+2 = 33

Simplifying this equation gives 3x + 3 = 33

Subtract three from both sides: 3x = 30

Divide both sides by three gives: x = 10

So the smallest number is ten.

Example 2

Two consecutive numbers multiplied together give the answer forty two. What is the smallest of those numbers?

Let the smallest number be x.

The other number can be written as x+1.

The product of the numbers is x(x+1) = 42

Expanding the brackets gives: x2 + x = 42

x2 + x - 42 = 0

(x + 7)(x - 6) = 0

Taking the positive answer; the smallest number is six.

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