The sum of all natural numbers lying between 100 and 500, which are divisible by 8 is ____.

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Accepted Answer

The sum of all natural numbers lying between 100 and 500, which are divisible by 8 is 15000.We need to find the sum of all natural numbers lying between 100 and 500, which are divisible by 8.We know,The formula of the sum of first n terms of an A.P is,

S
    n
   
   =
    n
    2

2
      a
      1
     
     +
      
       n−1
     d
   
   or

S
    n
   
   =
    n
    2

a
      1
     
     +L
   
   Where,The first term is a.The common difference is d.The number of terms are n.Here,

a
    1

is the first term, n is the number of terms in A.P, d is the common difference and L is the last term of the series.The series of natural numbers lying between 100 and 500 which are divisible by 8 are,

A.P=104, 112, 120,........., 496
   The first term of the series is

a

1

=104
  . The last term of the series is

a

n

=496
  . The common difference of the series is,

d=112−104

⇒d=8

.Therefore,

a
      n
     
     =
      a
      1
     
     +
      
       n−1
     d

⇒496=104+
      
       n−1
     8

⇒496−104=
      
       n−1
     8

⇒
      
       392
      8
     
     +1=n

⇒
      
       392+8
      8
     
     =n

⇒
      
       400
      8
     
     =n

⇒50=n

Now, the sum will be,

S
      n
     
     =
      n
      2

a
        1
       
       +L
                
      
       ∵
        a
        n
       
       =L

⇒
      S
      
       50
     
     =
      
       50
      2

104+496

⇒
      S
      
       50
     
     =15000

So, the sum of all natural numbers lying between 100 and 500 and divisible by 8 is 15000.

The sum of all natural numbers lying between 100 and 500, which are divisible by 8 is ____.

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