Two Consecutive Numbers

Introduction :

A number is a mathematical object used in counting and measuring. A notational symbol which represents a number is called a numeral, but in common usage the word number is used for both the abstract object and the symbol, as well as for the word for the number. In mathematics, the definition of number has been extended over the years to include such numbers as

0

• natural numbers
• rational numbers
• irrational numbers
• complex numbers. (Source: From Wikipedia)

In a set of numbers, two consecutive numbers are, a number and the number next to it. For example 1 and 2 are two consecutive numbers, -1 and -2 are also two consecutive numbers. Two consecutive numbers can be expressed algebraically as, x and x+1.

Example for Two Consecutive Numbers

Ex :  The sum of two consecutive numbers are 35. What are those numbers?

Sol :   let x be the number, so, x+1 is its consecutive number.

The sum of two consecutive numbers are 35.

So, x +(x + 1) = 35

x + x + 1 = 35

2x + 1 = 35

Subtract 1 on both sides

2x + 1 - 1 = 35 - 1

2x = 34

Divide by 2 on both sides,

`(2x)/2` = `34/2`

x = 17

so, the numbers are 17 and 17 + 1

The two consecutive numbers are 17, and 18.

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More Examples for Two Consecutive Numbers

Ex : The product of two consecutive numbers are 600. Find those two consecutive numbers.

Sol :  Let x be a number and x + 1 be it's consecutive number.

We know the product of two consecutive numbers is 600.

So, x(x + 1) = 600

x^2 + x = 600

subtract 600 on both sides,

x^2 + x - 600 = 0

x^2 + 25x - 24x - 600 = 0

x(x + 25) - 24(x + 25) = 0

(x + 25)(x - 24) = 0

i.e. x + 25 = 0 or x - 24 = 0

x = -25 or x = 24

There are two possible answers as follows,

The two consecutive numbers are

Ans 1: 24 and 25

Ans 2: -25 and  -24