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  4. The sum of all odd numbers between 1 and 1000 which are divisible by 3 is

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Q. The sum of all odd numbers between $ 1 $ and $ 1000 $ which are divisible by $ 3 $ is

UPSEEUPSEE 2009

Solution:

The required numbers are $3,9,15, \ldots \ldots, 999$
Here, $ l=a+(n-1) d $
$ \therefore 999= 3+(n-1) 6 $
$ \Rightarrow 6 n=1002 \Rightarrow n=167 $
$\therefore S=\frac{n}{2}[2 a+(n-1) d] $
$ =\frac{167}{2}(6+166 \times 6) $
$ =\frac{167}{2}(1002)$
$=83667$