Question

Which term of A.P. $20,19\frac{1}{4},18\frac{1}{2}$,..... is first negative term?

• A. $!8$th
• B. $15$th
• C. $28$th
• D. $27$th

Answer 1

Answer: (C)

$28$th

$20,19\frac{1}{4},18\frac{1}{2},....$
or $20,\frac{77}{4},\frac{37}{2},....$
$a=20$
$d=\frac{77}{4}-20=\frac{-3}{4}$
Let $n^{th}$ term of A.P. be first negative term
So, $20+(n-1)\left(\frac{-3}{4}\right)<0$
$\Rightarrow 80-3n+3<0$
$\Rightarrow 3n>83$
$\Rightarrow n>27\frac{2}{3}$
Hence, ${28}^{th}$ term is first negative term.
(Option $3$).