Q. 134.5( 12 Votes )

Find the sum of all natural numbers between 200 and 400 which are divisible by 7.

Answer :

Natural numbers between 200 and 400 which are divisible by 7 are 203, 210, 217, …, 399.

Sum of these numbers forms an arithmetic series 203 + 210 + 217 + … + 399.


Here, first term = a = 203


Common difference = d = 7


an = a + (n - 1)d


399 = 203 + (n - 1)7


399 = 7n + 196


7n = 203


n = 29


there are 29 terms in the AP.


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


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


Therefore sum of 28 terms of this arithmetic series is given by:


S29 = [2(203) + (29 - 1)(7)]


= (29/2) [406 + 196]


=(29/2) × 502


= 7279


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