The sum of 6 consecutive even numbers is 126. What is the fourth number in this sequence?

Solution:

We need to find out the second number  from  consecutive even number sequence.

 

                      Step-1:

We have to have knowledge about even number . If you divide a even number by 2 ,you will get a remainder of 0.

Now you have to understand about consecutive even number.The difference between two consecutive even number  is always 2.

 

 

                Step-2:

Say,the first even number is x.

So ,the second even number will be x+ 2. Thus, the third , fourth , fifth ,and sixth consecutive even number will be x+4 , x +6 , x+ 8 and x+10 respectively.

Have a look here.

The six consecutive even numbers are x, x+2,x+4 , x+6 , x +8 ,x+10 respectively.

 

                     Step-3:

According to the conditions,the sum of 6 consecutive even numbers will be 126.

 

So, we are getting the following equation

 

x +( x+2)+(x+4) +(x+6 )+(x+8) +(x+10) = 126

Or,6x +30 = 126

Or,6x + 30 – 30 = 126 - 30 [ Deduct 30 from both sides ]

Or, 6x + 0 = 96

Or, 6x = 96

Or, 6x/6 = 96/6

[Divide both sides by 6]

Or, x = 16

Now put the value of x here:

x, x+2,x+4 , x+6, x+8 , x+10

= 16, 16+2 , 16+4, 16 +6,16+8,16+10

=16,    18,     20,      22 ,  24,  26

So, the fourth number of this sequence is 22.

Answer:22

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