Find the n^{th} term of the H.P. whose first | vedclass

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Question

(A) The first term of the $H.P.$ is $6$ and the second term is $3$.Therefore,the first and second terms of the corresponding $A.P.$ are $\frac{1}{6}$

Vedclass · Accepted Answer

$\frac{6}{n}$

Vedclass · Answer

(A) The first term of the $H.P.$ is $6$ and the second term is $3$.Therefore,the first and second terms of the corresponding $A.P.$ are $\frac{1}{6}$ and $\frac{1}{3}$.For this $A.P.$,the first term $a = \frac{1}{6}$ and the common difference $d = \frac{1}{3} - \frac{1}{6} = \frac{2-1}{6} = \frac{1}{6}$.The $n^{th}$ term of the $A.P.$ is given by $a_n = a + (n-1)d$.$a_n = \frac{1}{6} + (n-1)\frac{1}{6} = \frac{1 + n - 1}{6} = \frac{n}{6}$.Since the $n^{th}$ term of an $H.P.$ is the reciprocal of the $n^{th}$ term of the corresponding $A.P.$,the $n^{th}$ term of the $H.P.$ is $\frac{6}{n}$.

Find the $n^{th}$ term of the $H.P.$ whose first two terms are $6$ and $3,$ respectively.

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