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