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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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.