Question

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

Answer 1

Here, $a=20d=19\frac{1}{4}-20=\frac{-3}{4}$

Let nth term be its first negative term.

So, $20+(n-1)\left(\frac{-3}{4}\right)<0\Rightarrow 80-3n+3<0\Rightarrow 83<3n\Rightarrow n>\frac{83}{3}\Rightarrow n>27.67$

So, n = 28