The sum of 6 consecutive even numbers is 270. What is the second 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 270.

 

So, we are getting the following equation

 

x +( x+2)+(x+4) +(x+6 )+(x+8) +(x+10) = 270

Or,6x +30 = 270

Or,6x + 30 – 30 = 270 -30[ Deduct 30 from both sides ]

Or, 6x + 0 = 240

Or, 6x = 240

Or, 6x/6 = 240/6

[Divide both sides by 6]

Or, x = 40

Now put the value of x here:

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

= 40, 40+2 , 40+4, 40 +6,40+8,40+10

=40,    42,     44,      46 ,  48, 50

So, the second number of this sequence is 42.

Answer:42

Next