Question

Find the sum of the number that is divisible by 2 as well as 5 between 1 to 500.

Answer 1

We have to find the number between $1$ to $500$ divisible by $2$ & $5$

First we will find the number divisible by $2$

$I.e2,4,6,8,........498$

$A_n=498=a+(n-1)d$

$=2+(n-1)2$

$\Rightarrow (n-1)2=496$

$\therefore$ Sum of $249$ form $=\frac{249}{2}[2\times 2+(248\left)2\right]$

$=37350$

Now we will find the number divisible by $1$ and $5$

$5,10,15,.........,495$

They are in $AP$

$a_n=495=5+(n-1)5$

$\Rightarrow (n-1)=\frac{490}{5}+1$

$\Rightarrow n=98+1=99$

$\therefore$ Sum of $100$ term $=\frac{100}{2}[2\times 5+(99\left)5\right]$

$=\frac{99}{2}[2\times 5+98\times 5]$

$=25250$

Now number divisible by $10,20,.........490$

$a_n=490=10+(n-1)10$

$\Rightarrow n-1=\frac{480}{10}$

$\Rightarrow n=49$

Sum $=\frac{49}{2}[2\times 10+(48\left)\right(10\left)\right]=\frac{49}{2}\times \left[500\right]$

$=49\times 250$

$=12250$