Q. 265.0( 1 Vote )

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

Answer :

The numbers lying between 300 and 700 which are multiples of 9 are


306, 315, 324,…, 693


a2 – a1 = 315 – 306 = 9


a3 – a2 = 324 – 315 = 9


a3 – a2 = a2 – a1 = 9


Therefore, the series is in AP


Here, a = 306, d = 9 and an = 693


We know that,


an = a + (n – 1)d


693 = 306 + (n – 1)9


693 - 306 = (n – 1)9


387 = (n – 1)9


43 = (n – 1)


n = 44


Now, we have to find the sum of this AP




S44 = 22[612 + 387]


S44 = 22[999]


S44 = 21978


Hence, the sum of all numbers lying between 300 and 700 is 21978.


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