Question

Find the first negative term of sequence $999,995,991,987,$
$...$

Answer 1

$AP=999,995,991,987,...$

Here,$a=999,d=995-999=-4$

$a_n<0$

$\Rightarrow a+(n-1)d<0$

$\Rightarrow 999+(n-1)(-4)<0$

$\Rightarrow 999-4n+4<0$

$\Rightarrow 1003-4n<0$

$\Rightarrow 1003<4n$

$\Rightarrow \frac{1003}{4}<n$

$\Rightarrow n>250.75$

Nearest term greater than $250.75$ is $251$

So, ${251}^{st}$ term is the first negative term

Now, we will find the ${251}^{st}$ term

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

$\Rightarrow a_{251}=999+(251-1)(-4)$

$\Rightarrow a_{251}=999+250\times -4$

$\Rightarrow a_{251}=999-1000$

$\Rightarrow a_{251}=-1$

$\therefore ,-1$ is the first negative term of the given AP.