Question

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

Answer 1

$a_3\Rightarrow a+2d=\mathrm{4...}\left(1\right)$

$a_4\Rightarrow a+8d=-8...\left(2\right)$

Subtracting (2) from (1), we get

$a+2d=4$

$-a+8d=-8$

_________________

$-6d=12$

$d=-2$

$\therefore a=4-2d=4+(-2)(-2)\Rightarrow a=8$

$\therefore A.P\Rightarrow 8,6,4,2,0,-2,...$

$\therefore$ As we can see, $a_5=0$

$\therefore 5^{th}$ term in this A.P is 0.