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Q.

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


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Detailed Solution

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