Question

The number of even integers lie in between $51$ and $1000$ which are divisible by $15$ is

Answer 1

First term will be $60.$
Last term will be $990.$
So, the sequence which is divisible by $15$ is
$60,75,90,\cdots ,975,990$
then sequence of even integres
$60,90,\cdots ,990$
We know,
$n=\frac{l-a}{d}+1\cdots \left(i\right)$
where $l=990,a=60$ and $d=30$
Put all the above values in eq.$\left(i\right),$ we get
$\Rightarrow n=\frac{990-60}{30}+1$
$\Rightarrow n=\frac{930}{30}+1$
$\Rightarrow n=31+1=32$