Question

The sum of all odd integers between $2$ and $50$ divisible by $3$ is

• A. $192$
• B. $216$
• C. $168$
• D. $240$

Answer 1

The correct option is A $192$

The odd intergers between 2 and 50 divisible by 3 are $3,9,15,......45$
This sequence forms an AP with first term $a=3$ and common difference $d=9-3=6$
Since, $l=a+(n-1)d$
$\Rightarrow 45=3+(n-1)6$
$\Rightarrow 42=(n-1)6$
$\Rightarrow 7=n-1$
$\Rightarrow n=8$
Number of terms in given sequence are 8.
$S_n=\frac{n}{2}(a+l)$
$\Rightarrow S_n=\frac{8}{2}(3+45)$
$\Rightarrow S_n=4\left(48\right)$
$\Rightarrow S_n=192$
$\therefore$ Option A is correct.