Question

Find the sum of all odd integers between $2$ and $100$ divisible by $3$.

Answer 1

Such integers are $3,9,15,21,\dots ...99$

This is an A.P with $a=3$

$d=6$

$a_n=l=99$

$a_n=a+(n-1)d$

$99=3+(n-1)6$

$\Rightarrow n=17$

${\S }_n=\frac{n}{2}(a+l)$

$S_{17}=\frac{17}{2}(3+99)=867$.