Question

Which term of the progression $20,19\frac{1}{4},18\frac{1}{2},17\frac{3}{4}......$ is the first negative term?

Answer 1

Given: $20,19\frac{1}{4},18\frac{1}{2},17\frac{3}{4}......$
Here,
$a=20$ and $d=19\frac{1}{4}-20=\frac{77-80}{4}=-\frac{3}{4}$

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

Now, $a_n<0$

$\Rightarrow a_n=20+(n-1)(-\frac{3}{4})<0$

$\Rightarrow 20-\frac{3}{4}n+\frac{3}{4}<0$

$\Rightarrow -\frac{3}{4}n+\frac{83}{4}<0$

$\Rightarrow \frac{3}{4}n>\frac{83}{4}$

$\Rightarrow n>\frac{83}{3}$

$\Rightarrow n>27.67$

$\Rightarrow n\ge 28$
Thus, the first negative term will be $a_{28}$.