Question

If the 9th term of an AP is zero, then the ratio of 29th term to 19th term is

• A. 1 : 2
• B. 1 : 3
• C. 2 : 1
• D. 3 : 1
• E. 9 : 1

Answer 1

Answer: (C)

Given, $T_9=0$ and $\frac{T_{29}}{T_{19}}=?$ Let the first term and common difference of an AP is a, d respectively.
Then, $a+8d=0$ ...(i) $\frac{T_{29}}{T_{19}}=\frac{a+28d}{a+18d}$
$=\frac{-8d+28d}{-8d+18d}=\frac{20d}{10d}=\frac{2}{1}$
$\Rightarrow$ $T_{29}:T_{19}=2:1$