Question

If the $3rd$ and the $9th$ terms of an $AP$ are $4$ and $-8$ respectively, which term of this $AP$ is zero?

Answer 1

Formula:

$T_n=a+(n-1)d$

Given,

$T_9=a+8d=-8$.......(1)

$T_3=a+2d=4$........(2)

(1)-(2) gives,

$d=-2$

From (2)

$a=4-2(-2)=8$

$0=8+(n-1)(-2)$

$2(n-1)=8$

$\Rightarrow n=5$

Therefore 5th term is zero.