Question

Which term of the A.P. $17,14,11$ is the first negative terms.

Answer 1

Given,

$a=17$

$d=14-17=-3$

$T_n<0$

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

$17+(n-1)(-3)<0$

$17-n+3<0$

$n>\frac{20}{3}$

$\Rightarrow n=7$

7th term is the first negative term

$T_7=17+(7-1)(-3)=-1$

Hence verified.