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

Question

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 these

Tardigrade Admin · Accepted Answer

The required numbers are 3,9,15, ldots ldots, 999 Here, l=a+(n-1) d ∴ 999= 3+(n-1) 6 ⇒ 6 n=1002 ⇒ n=167 ∴ S=(n/2)[2 a+(n-1) d] =(167/2)(6+166 × 6) =(167/2)(1002) =83667

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

83667

90000

83660

None of these

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

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