Question

Which term of the AP:22,19,16....... is its first negative term?

Answer 1

We have,

$a=22$

$d=-3$

Given that,

The first negative term is

$a_n<0$

So,

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

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

$\Rightarrow 22+(n-1)(-3)<0$

$\Rightarrow 22-3n+3<0$

$\Rightarrow 25-3n<0$

$\Rightarrow 25<3n$

$\Rightarrow \frac{25}{3}<n$

$\Rightarrow n>8.33$

So, the natural number is $9$.

Therefore, $9^{th}term$ is the first negative term of the given A.P.

This is the answer.