If the 9^{th} term of an A.P. is zero,then th | vedclass

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(B) Let the first term of the $A.P.$ be $a$ and the common difference be $d$.The $n^{th}$ term of an $A.P.$ is given by $a_n = a + (n - 1)d$.Given tha

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$2:1$

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(B) Let the first term of the $A.P.$ be $a$ and the common difference be $d$.The $n^{th}$ term of an $A.P.$ is given by $a_n = a + (n - 1)d$.Given that the $9^{th}$ term is zero:$a_9 = a + (9 - 1)d = 0$$a + 8d = 0 \Rightarrow a = -8d$.Now,we need to find the ratio of the $29^{th}$ term to the $19^{th}$ term:$a_{29} = a + 28d = -8d + 28d = 20d$.$a_{19} = a + 18d = -8d + 18d = 10d$.Ratio $= \frac{a_{29}}{a_{19}} = \frac{20d}{10d} = \frac{2}{1}$.Thus,the ratio is $2:1$.

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

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