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

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

KEAMKEAM 2011

Solution:

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 $