Q. The sum of all odd numbers between 1 and 1000 which are divisible by 3, is
A) 83667
B) 90000
C) 83660
D) None of the above
Explanation
(a)
The required numbers are
3,9,15,…,999
Here, $l = a + (n - 1)d$
$\therefore 999 = 3 + (n - 1)6$
$\Rightarrow 6n = 1002 \Rightarrow n = 167$
$\therefore S = \frac{n}{2}\lbrack 2a + (n - 1)d\rbrack$
$= \frac{167}{2}(6 + 166 \times 6)$
$= \frac{167}{2}(1002)$
$= 83667$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.