Question

Find that sum of first $30$ integer divisible by $6$.

Answer 1

The numbers that are divisible by $6$ are $6,12,18,24,30,36,.......$
Where, first term, $a=6$,
common difference, $d=12-6=6$
As we know that the sum of first $n$ numbers in an AP is given by
$S_n=\frac{n}{2}(2a+(n-1\left)d\right)$........(i)
Substitute $n=30,a=6$ and $d=6$ in the above equation(i) to get the required sum.
$\Rightarrow S_{30}=\frac{30}{2}\left[\right(2\times 6)+(30-1\left)6\right]$
$=15[12+29(6\left)\right]$
$=15[12+174]$
$=15\left(186\right)$
$=2790$
Therefore, the sum of first $30$ positive integers divisible by $6$ is $2790$.