Question

Find the sum of odd interges from 1 to 2001 ,

Answer 1

All odd intergers from 1 to 1000 are 1, 3, 5, 7, ........... 2001,

Here a = 1, d = 3 - 1 = 2, $a_n$ = 2001.

We have that $a_n=a+(n-1)d$

$\therefore$ 2001 = $1+(n-1)\times 2$

$\Rightarrow 2001-1=(n-1)\times 2\Rightarrow \frac{2000}{2}=n-1$

$\Rightarrow n=1000+1=1001$

Now, $s_n=\frac{n}{2}[a+1]$

$\therefore s_{1001}=\frac{1001}{2}[1+2001]=\frac{1001}{2}\times 2002$

= $1002001[\therefore l=a_n=2001]$