Question

If $9^{th}$ term of an A.P be zero, then the ratio of its ${29}^{th}$ and ${19}^{th}$ term is

• A. $1:2$
• B. $2:1$
• C. $1:3$
• D. $3:1$

Answer 1

The correct option is B $2:1$

Given, $a_9=0$
$\Rightarrow a_9=a+8d$
$\Rightarrow a+8d=0$
$\Rightarrow a=-8d$ .......(i)
$a_{29}=a+28d$
By (i), we have
$\Rightarrow a_{29}=-8d+28d$

$\Rightarrow 20d$
$a_{19}=a+18d$
By equation (i), we have
$a_{19}=-8d+18d$

$\Rightarrow 10d$
$\Rightarrow \frac{a_{29}}{a_{19}}=\frac{20d}{10d}=\frac{2}{1}=2:1$