Q. 164.9( 7 Votes )

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

Answer :

Multiples of 9 lying between 300 and 700 are 306, 315, 324, …, 693.

Sum of these numbers forms an arithmetic series 306 + 315 + 324 + … + 693.


Here, first term = a = 306


Common difference = d = 9


We first find the number of terms in the series.


Here, last term = l = 693


693 = a + (n - 1)d


693 = 306 + (n - 1)9


693 - 306 = 9n - 9


387 = 9n - 9


387 + 9 = 9n


9n = 396


n = 44


Now, Sum of n terms of this arithmetic series is given by:


Sn = [2a + (n - 1)d]


Therefore sum of 44 terms of this arithmetic series is given by:


S44 = [2(306) + (44 - 1)(9)]


= 22 × [612 + 387]


= 22 × 999


= 21978


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