The sum of 4 consecutive even numbers is 36. What is the first number in this sequence?

Solution:

We need to find out the first 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 and fourth consecutive even number will be x+4  and x +6 respectively.

Have a look here.

The four consecutive even number are x, x+2,x+4 , x+6 respectively.

 

                     Step-3:

According to the conditions,the sum of 4 consecutive even number will be 36.

 

So, we are getting the following equation

 

x + x+2+x+4 +x+6 =36

Or,4x +12 = 36

Or,4x + 12 – 12 = 36 -12  [ Deduct 12 from both sides ]

Or, 4x + 0 = 24

Or, 4x = 24

Or, 4x/4 = 24/4 [Divide both sides by 4]

Or, x = 6

Now put the value of x here:

x, x+2,x+4 , x+6

= 6, 6+2 , 6+4, 6 +6

=6,8,10,12

So, the first number of this sequence is 6.

Answer:6

Proof: 6+8+10+12 =36( proved)