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.

 Two consecutive numbers multiplied together give the answer forty two. What is the smallest of those numbers?42 Working: Two consecutive numbers multiplied together give the answer one hundred and eighty two. What is the smallest of those numbers?182 Working: Two consecutive numbers multiplied together give the answer five hundred and six. What is the smallest of those numbers?506 Working: Two consecutive numbers multiplied together give the answer one thousand, one hundred and ninety. What is the smallest of those numbers?1190 Working: Two consecutive numbers multiplied together give the answer two thousand, five hundred and fifty. What is the smallest of those numbers?2550 Working: Two consecutive numbers multiplied together give the answer four thousand, six hundred and ninety two. What is the smallest of those numbers?4692 Working: Three consecutive numbers multiplied together give the answer seven hundred and fifty three thousand, four hundred and eighty. What is the smallest of those numbers?753480 Working: The largest of four consecutive numbers is fourteen. What is the product of those numbers?14 Working: Three consecutive even numbers multiply together to give a product of one thousand, six hundred and eighty. What is the largest of those numbers?1680 Working: If a, b and c are three consecutive positive odd numbers and the square of b is thirty five more than the sum of a and c what is a?35 Working:
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Level 2 - Questions about the multiplication of consecutive numbers

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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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