SOLUTION: Find the sum of all positive integers less than 1000 that are divisible by 3 but not by 2.

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Question 257633: Find the sum of all positive integers less than 1000 that are divisible by 3 but not by 2.
Answer by vksarvepalli(154) About Me  (Show Source):
You can put this solution on YOUR website!
the no.s should not be multiples of 2
so no even no.s
so we need to find the sum of all odd multiples of 3
that is sum = 3*1 + 3*3 + 3*5 + 3*7 + 3*9 + .........+ 3*333
= 3*(1+3+5+7+...................+333)
the series in the brackets is an arithmetic progression with the first term being 1 and common difference 2 and has 167 terms (1=2*1-1 and 333=2*167-1)
the sum is 167%2F2%2A%281%2B333%29 = 27889
also we can find the sum from the fact that sum of n consecutive odd no.s is n%5E2
so the required sum now is 3*27889= 83667 is the answer