The sum of 5 consecutive integers is 500. What is the third number in this sequence?

Question

a math question

Answer 1

x + 1  plus  x + 2  plus  x + 3  plus x + 4  plus x +5   =  500

5x + 15  =  500    'Simplify

     -  15  =  -15    'Solve for x

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5x          =  485    'arrived here with subt.property of equality

 

5x          =  485    'rewrite

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5                   5    ' division property of equality

 

 x           =   97

 

x + 1 = 98

x + 2 = 99

x + 3 = 100

 

 

Answer 2

Let the 1st integer = x

Let the 2nd = x + 1

Let the 3rd = x + 2

Let the 4th = x + 3

Let the 5th = x + 4

 

x + (x + 1) + (x + 2) + (x + 2) + (x + 3) + (x + 4) = 500

 

5x + 10 = 500

5x = 490

  x = 98

 

Substitute this value of x in (x + 2).

 

The third number is 100.