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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 twenty one. What is the smallest of those numbers?21

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Three consecutive numbers added together give the answer thirty nine. What is the smallest of those numbers?39

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Three consecutive numbers added together give the answer sixty six. What is the smallest of those numbers?66

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Five consecutive numbers added together give the answer one hundred and eighty five. What is the smallest of those numbers?185

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Five consecutive numbers added together give the answer two hundred and seventy. What is the smallest of those numbers?270

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The largest of five consecutive numbers is two hundred and thirty eight. What is the smallest of those numbers?238

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The largest of five consecutive numbers is fourteen. What is the sum of those numbers?14

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The largest of ten consecutive numbers is twenty. What is the sum of those numbers?20

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Seven consecutive even numbers add up to one hundred and eighty two. What is the smallest of those numbers?182

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Four consecutive even numbers have a mean of twenty three. What is the smallest of those numbers?23

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Instructions

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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.

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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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