Question

Which term of the sequence $24,23\frac{1}{4},22\frac{1}{2},21\frac{3}{4},...$ is the first negative term?

Answer 1

$24,23\frac{1}{4},22\frac{1}{2},21\frac{3}{4},...$

or $\frac{96}{4},\frac{93}{4},\frac{90}{4},\frac{87}{4},...$

or $96,93,90,87,...$ are in A.P

$a=96$, $d=93-96=-3$

According to question,

$96+(n-1)(-3)<0$

$\Rightarrow 99-3n<0$

$\Rightarrow 3n>99$

$\Rightarrow n>33$

The first integer$>33$ is $34$

$\therefore t_{34}$ is the first negative term.