Q. 44.3( 27 Votes )

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

Answer :

The numbers lying between 200 and 400 which are divisible by 7


are as follows: -


203, 210, 217, … 399


Since the common difference between the consecutive terms is constant. Thus, the above sequence is an A.P.


First term, a = 203


Last term, l = 399


Common difference, d = 7


Let the number of terms of the A.P. be n.


an = 399 = a + (n –1) d


399 = 203 + (n –1) 7


7 (n –1) = 196


n –1 = 28


n = 29


We know that -


Sum of n terms of an A.P(Sn) = (n/2)[a + l]


S29 = (29/2)[203 + 399]


= (29/2)[602]


= 29 × 301


= 8729


Thus, the required sum is 8729.


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