Question

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

Answer 1

Given that, $a_3=4$, $a_9=-8$

We know that,

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

$a_3=a+(3-1)d$

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

And

$a_9=a+(9-1)d$

$-8=a+8d$ ... (ii)

On subtracting equation (i) from (ii), we get,

$-12=6d$

$d=-2$

From equation (i), we get,

$4=a+2(-2)$

$\Rightarrow a=8$

Let $n^{th}$ term of this A.P. be zero.

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

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

$\Rightarrow n=5$

Hence, $5$th term of this A.P. is $0.$