If the 7^{th} term of a H.P. is frac{1}{10} a | vedclass

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(D) Let the $H.P.$ be the reciprocal of an $A.P.$ with first term $a$ and common difference $d$.Given that the $7^{th}$ term of $H.P.$ is $\frac{1}{10

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$\frac{1}{49}$

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(D) Let the $H.P.$ be the reciprocal of an $A.P.$ with first term $a$ and common difference $d$.Given that the $7^{th}$ term of $H.P.$ is $\frac{1}{10}$,the $7^{th}$ term of the corresponding $A.P.$ is $10$.So,$a + 6d = 10$  $(i)$Given that the $12^{th}$ term of $H.P.$ is $\frac{1}{25}$,the $12^{th}$ term of the corresponding $A.P.$ is $25$.So,$a + 11d = 25$  $(ii)$Subtracting $(i)$ from $(ii)$:$(a + 11d) - (a + 6d) = 25 - 10$$5d = 15 \Rightarrow d = 3$Substituting $d = 3$ in $(i)$:$a + 6(3) = 10$ $\Rightarrow a + 18 = 10$ $\Rightarrow a = -8$Now,the $20^{th}$ term of the $A.P.$ is $T_{20} = a + 19d = -8 + 19(3) = -8 + 57 = 49$.Therefore,the $20^{th}$ term of the $H.P.$ is the reciprocal of $49$,which is $\frac{1}{49}$.

If the $7^{th}$ term of a $H.P.$ is $\frac{1}{10}$ and the $12^{th}$ term is $\frac{1}{25}$,then the $20^{th}$ term is

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