Sum of Two Consecutive Numbers

Introduction :

Let us see the problems on sum of two consecutive numbers, after giving the explanation about consecutive numbers. the consecutive numbers are the numbers in continuous order, without gaps, from smallest to largest.

Let x be a number the consecutive number for x is x+1 and the next consecutive number for x+1 is (x+1)+1

ie., x+2

General form of consecutive numbers :  x, x+1, x+2, x+3,.........

If x is 3 ie., 3, 3+1, 3+2, 3+3 are consecutive numbers

ie., 3,4,5,6,...........are consecutive numbers


Sum of Two Consecutive even and Odd Numbers

Consecutive Even and Odd numbers

Till now we have seen the consecutive number for only natural numbers . Now let us discuss about consecutive even numbers and odd numbers.

Consecutive Even Numbers: We know , a even number is a number which is divisible by 2. Let the number be x and even number is "2x"

So the consecutive even number for 2x are 2x+2,2x+4,..........

If x is 1, then 2(1),2(1)+2,2(1)+4,....... is

2,4,6,.........

Consecutive Odd Numbers: Odd number is a number which is not divisible by 2 and remainder is 1. If x is any number 2x+1 is odd number .

The consecutive odd numbers are 2x+1,(2x+1)+2,[(2x+1)+2]+2

2x+1,2x+3,2x+5,........

so if x is 0 the consecutive numbers are 2(0)+1,2(0)+3,2(0)+5 ,... are

1,3,5,.......

Example Problems on Sum of Two Consecutive Numbers
Problem on sum of two consecutive numbers:

The sum of two consecutive integers is 15 . Find the two numbers.

Let x be one of the consecutive numbers.

x+1 is the other consecutive number

The sum of these two consecutive numbers is x+(x+1)= x+x+1= 2x+1

Given the sum is 15

Therefore 2x+1= 15

=> 2x= 15-1 =14

=> 2x= 14

=> x= 14/2=7

=>x=7

The consecutive number is x+1=8

The two consecutive numbers are 7,8.

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Example Problems on Sum of Two Consecutive even Numbers

Problem : The sum of two consecutive even numbers is 14. Find the two numbers.

let the even number be 2x and the consecutive even number is 2x+2

sum of consecutive even numbers is 2x+2x+2= 4x+2

Given the sum is 14

Therefore 4x+2= 14

=>4x= 14-2

=>4x=12

=>x=12/4=3

=>x=3

The consecutive even numbers is 2(3),2(3)+2 is 6,8

Example on Sum of Two Consecutive Odd Numbers
problem: The sum of consecutive odd numbers is 8. Find the numbers?

let the odd number is 2x+1 and the consecutive odd number for 2x+1 is 2x+3

The sum of consecutive odd numbers is 2x+1+2x+3= 4x+4

Given the sum is 8

Therefore

4x+4=8

=> 4x=8-4=4

=>4x=4

=>x=4/4=1

=>x=1

The consecutive odd numbers are 2(1)+1,2(1)+3

ie., 3,5 are consecutive odd numbers.