The sum of 5 consecutive even numbers is 100. What is the first number in this sequence?

 

Solution:

We need to find out the third 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 and fifth consecutive even number will be x+4 , x +6 and x+ 8 respectively.

Have a look here.

The five consecutive even numbers are x, x+2,x+4 , x+6 and x +8  respectively.

 

                     Step-3:

According to the conditions,the sum of 5 consecutive even number will be 100.

 

So, we are getting the following equation

 

x + x+2+x+4 +x+6 +x+8 =100

Or,5x +20 = 100

Or,5x + 20 – 20 = 100 -20[ Deduct 20 from both sides ]

Or, 5x + 0 = 80

Or, 5x = 80

Or, 5x/5 = 80/5

[Divide both sides by 5]

Or, x = 16

Now put the value of x here:

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

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

= 16,    18,     20,      22 ,  24

So, the first number of this sequence is 16.

Answer: 16

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