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(B) sequence is a harmonic progression $(H.P.)$ if the reciprocals of its terms form an arithmetic progression $(A.P.)$.Given the first term of the $H

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$1/29$

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(B) sequence is a harmonic progression $(H.P.)$ if the reciprocals of its terms form an arithmetic progression $(A.P.)$.Given the first term of the $H.P.$ is $1/7$,the first term of the corresponding $A.P.$ is $a = 7$.The second term of the $H.P.$ is $1/9$,so the second term of the $A.P.$ is $a + d = 9$.Calculating the common difference $d$: $d = 9 - 7 = 2$.The $n^{th}$ term of an $A.P.$ is given by $T_n = a + (n - 1)d$.For the $12^{th}$ term of the $A.P.$: $T_{12} = 7 + (12 - 1) 	imes 2 = 7 + 11 	imes 2 = 7 + 22 = 29$.Since the $12^{th}$ term of the $H.P.$ is the reciprocal of the $12^{th}$ term of the $A.P.$,the $12^{th}$ term of the $H.P.$ is $1/29$.

The first term of a harmonic progression is $1/7$ and the second term is $1/9$. The $12^{th}$ term is

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