# Consecutive Numbers

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

##### Level 1Level 2Exam-StyleDescriptionHelpMore 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.

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## Instructions

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## Teachers

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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.

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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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