Q. 75.0( 1 Vote )

Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667

Answer :

according to given conditions the sequence is 3, 9, 15, 21….999

Given an AP whose first term is 3 and d is 6. Hence sum is given by


To prove: the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667


Hence the sum is given by the formula


Now for the finding number of terms, the formula is




n = 167


Substituting n is the sum formula we get



s = 83667


Hence, Proved.


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