Question

Which term of the AP: 53, 48, 43,... is the first negative term?

Answer 1

Here first term $a=53$ and common difference $d=-5$

Let the nth term of the given AP be the 1st negative term.

$\therefore a_n<0$

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

$\Rightarrow 53+(n-1)\times -5<0$

$\Rightarrow (n-1)\times -5<-53$

$\Rightarrow n-1>\frac{53}{5}$

$\Rightarrow n>\frac{58}{5}$

$\Rightarrow n>11\frac{3}{5}$

Since, $12$ is the natural number just greater than$11\frac{3}{5}$

So, $n=12$

$\therefore {12}^{th}$ term is first negative term.