A) 1 : 2
B) 1 : 3
C) 2 : 1
D) 3 : 1
E) 9 : 1
Correct Answer: C
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) \[\frac{{{T}_{29}}}{{{T}_{19}}}=\frac{a+28d}{a+18d}\] \[=\frac{-8d+28d}{-8d+18d}=\frac{20d}{10d}=\frac{2}{1}\] \[\Rightarrow \] \[{{T}_{29}}:{{T}_{19}}=2:1\]
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