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Deepak Bora
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Find the sum of all even numbers between 5 and 100.

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This is the Question Number 8 Of Exercise 11 C of RS Aggarwal Solution
ICSE & CBSE Board Question Based on Arithmetic Progression of RS Aggarwal
Here you have to find the
(i) sum of all even numbers
(ii) Between two numbers which is given

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  1. This answer was edited.

    So 100 will not be included in our case.
    So writing the sequence we get,
    => 6, 8, 10, 12, 14 …….., 98
    => a = 6, d = 2, = 98, n = ?
    Formula for calculating :
    a_n=a+(n-1)d
    => 98 = 6 + ( n – 1 ) 2
    => 98 – 6 = ( n – 1 ) 2
    => 92 = ( n – 1 ) 2
    => 92 / 2 = ( n – 1 )
    => 46 = ( n – 1 )
    => n = 46 + 1 = 47
    Hence there are 47 terms.
    Now, we know that Sum of n terms of an AP can be given as:
    S_n=n/2[a+a_n]
    So substituting in the equation we get,
    => Sum of 47 terms = ( 47 / 2 ) ( 6 + 98 )
    => Sum of 47 terms = ( 23.5 ) ( 104 )
    => Sum of 47 terms = 2444
    Hence the answer is 2444.

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