【 】The sum of 5 consecutive integers is 505. What is the third number in this sequence?

Solution:

The third number of this sequence is 101.

Explanation:

We need to find out the  third  number  from  consecutive integer numbers' sequence.

 

                      Step-1:

We have to have knowledge about integer number.An integer number does not have any fractional part.It can be positive or negative number.

Now you have to understand about consecutive integer number.The difference between two consecutive integer numbers  is always 1.

 

                Step-2:

Say,the first integer number is x.

So, the second integer number will be x+ 1. Thus, the third consecutive integer number will be x+2 .Besides,the fourth integer number will be x+3 and the fifth number will be x+4 .

Have a look here.

The five consecutive integer numbers are x, x+1,x+2 ,x+3 ,x+4 respectively.

                  Step-3:

According to the conditions,the sum of 5 consecutive integer numbers will be 505.

 

So, we are getting the following equation

 

x +( x+1)+(x+2) +(x+3) +(x+4)  = 505

Or, 5x + 10 = 505

Or, 5x + 10 -10  = 505 - 10[ Deduct 10 from both sides ]

Or, 5x + 0 = 495

Or, 5x = 495

Or, 5x/5 =  495/5

[Divide both sides by 5]

Or, x = 99

Now put the value of x here:

   x,     x+1,  x+2 , x+3  , x+4

= 99,  99+1 , 99+2 , 99+3,99 +4

99 ,   100,      101,           102,    103

So, the third number of this sequence is 101.

Answer: 101

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