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Deepak Bora
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Find the sum of all multiples of 9 lying between 300 and 700.

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An Important question based on Arithmetic progression Chapter of R.S Aggarwal book for ICSE & CBSE Board.
This is the Question Number 11 Exercise 11 C of RS Aggarwal Solution.
Here you have to find the all multiples of given digit which is lying between the given numbers.

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  1. The multiples of 9 between 300 and 700 :-
    306 , 315 , 324 ,….., 693
    First term = 306
    Common difference = 9
    nth term = 693
    a_n=a+(n-1)d
    693 = 306 + (n – 1)9
    693-306/9=n-1
    n-1=387/9
    (n – 1) = 43
    n = 43 + 1
    n = 44
    Using formula :-
    S_n=n/2(a+l)
    S_44=44/2(306+693)
    = 22 × 999
    = 21978

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