Skip to main content

the sum of three consecutive even numbers is 138

The example for consecutive even numbers is 2,4,6,8,10,. . . .
The above consecutive even number series can be written as
        2,2+2,2+4,2+6,2+8,2+10, . . . . .
In the above series if we replace 2 in every number by “x”.
Then the above series can be rewritten as
        X, X+2,X+4,X+6, X+8, X+10, X+12,. . . . . . .
From the above series we can written as
2 consecutive even numbers = X, X+2
3 consecutive even numbers  =        X, X+2,X+4
4 consecutive even numbers =  X, X+2,X+4,X+6
5 consecutive even numbers =   X, X+2,X+4,X+6, X+8
Now we see the following problem
the sum of three consecutive even numbers  is 138. what is the smallest/ biggest of these numbers
We can write three consecutive even number series as
 3 consecutive even numbers =   X, X+2,X+4.
   Sum of consecutive even numbers = X+ X+2+X+4
                                                              138=X+X+X+2+4
                                                              138= X+X+X+2+4
                                                             138= 3X+2+4
                                                             138=3X+6
                                                             138-6=3X
                                                             132=3X
It can be written as
                                                             3X=132
                                                               X= 132/3
                                                                  = 44
3 consecutive even numbers =   X, X+2,X+4
Substituting x =44
3 consecutive even numbers = 44, 44+2, 44+4
                                                    =  44, 46,48
from the above series smallest number =44.
From the above series biggest number = 48.
the sum of three consecutive even numbers is 138  then the biggest of these numbers = 48.

the sum of three consecutive even numbers is 138  then the smallest of these numbers = 44.

Comments

Popular posts from this blog

pythagoras triangle numbers from difference between two adjacent numbers

1 2 =1x1=1                           ---->3 2 2 =2x2=4                           ---->5 3 2 =3x3=9                           ---->7 4 2 =4x4= 16                           ----> 9 --->(pythagoras numbers 16+9=25 ==>  4 2 +3 2   = 5 2 ) 5 2 =5x5= 25                           ---->11  6 2 =6x6=36            ...

product two consecutive odd numbers

Product of two consecutive odd numbers : Even numbers are 1,3,5,7,9,11,13,15,17,19,21,23,25,..... Odd  number means when we divide a number with 2,then the remainder is equal to one. Difference between the two odd numbers is 1. Now we will discuss the product of two odd  numbers. Now the product of two even numbers assumed to be 5x7 can be written as (6-1)x(6+1).                              5x7= (6-1)x(6+1) From the above we write general formula as 5x7= (6-1)x(6+1)=6 2 -1 2  =36-1=35 Now we can observe the result as one less than the square number. So now we can observe the following table. Column 1&2 reprecent the adjacent odd numbers. Column 3 represent the product of two adjacent odd numbers. Column 4 represent  the nearest square number. This  will arrive by adding 1 to the product  of two odd ...

Average of first n even numbers

Even numbers are 2,4,6,8,10,…. Average = sum of elements/ no of elments Now we will see the sum of elements: Sum of first 2 even numbers: 2+4= 6= 2(2+1) Sum of first 3 even numbers: 2+4+6= 12= 3(3+1) Sum of first 4 even  numbers: 2+4+6+8=20= 4(4+1) Sum of first 5 even numbers: 2+4+6+8+10 = 30 = 5(5+1) Sum of first n even numbers: 2+4+6+8+10+. . . . .  n numbers= n(n+1) Now we will see average: Average of first 2 even numbers= (2+4)/2                                                           = 6/2                              ...