Question

Which term of the A. P. $17,16\frac{1}{5},15\frac{2}{5},14\frac{3}{5}....$ is first negative term?

Answer 1

$17,16\frac{1}{5},15\frac{2}{5},14\frac{3}{5}..........$

First term, $a=17$

common difference, $d=16\frac{1}{5}-17$

$d=\frac{81}{5}-17=-\frac{4}{5}$

Let the $n$th term is negative.

$a_n<0$

$a+(n-1)d<0$

$17-\frac{4}{5}(n-1)<0$

$-\frac{4}{5}(n-1)<-17$

$\frac{4}{5}(n-1)>17$

$4n-4>85$

$4n>89$

$n>\frac{89}{4}$

$n>22.25$

$n$ will be a positive integer. So, $23$rd term is the first negative term.