Question

The first negetive term in the sequence of $56,55\frac{1}{5},54\frac{2}{5},\cdots$

• A. ${71}^{th}$
• B. ${70}^{th}$
• C. ${72}^{th}$
• D. ${73}^{th}$

Answer 1

The correct option is C ${72}^{th}$

$56,55\frac{1}{5},54\frac{2}{5},\cdots$
$=\frac{280}{5},\frac{276}{5},\frac{272}{5},...$
Hence, the given sequence is in AP with common difference $d=-\frac{4}{5}$
To find the first negative term, $T_n<0$
$\Rightarrow a+(n-1)d<0$
$\Rightarrow 56+(n-1)(-\frac{4}{5})<0$
$\Rightarrow 280-4n+4<0$
$\Rightarrow 4n>284$
$\Rightarrow n>71$
Hence, first negative term is ${72}^{th}.$