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

Deepak BoraNewbie

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

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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.