If $a$ and $d$ are the first term and the common difference of the A.P respectively, then the $n^{t h}$ term of corresponding H.P is

a_{n} = a + (n - 1) d

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a_{n} = \frac{1}{a + (n - 1) d}

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a_{n} = \frac{a}{1 + (n - 1) d}

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a_{n} = \frac{a}{a + (n - 1) d}

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Solution

The correct option is C $a_{n} = \frac{1}{a + (n - 1) d}$
Given, $a$ and $d$ are the first term and the common difference of the A.P.
$∴ a, a + d, a + 2 d, . . . . . . . ., a + (n - 1) d$ forms an AP.
Since, if $a, b, c$ are in AP. then $\frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are in HP.
$∴ \frac{1}{a}, \frac{1}{a + d}, \frac{1}{a + 2 d}, . . . . . . . ., \frac{1}{a + (n - 1) d}$ are in HP.
$∴$ $n^{t h}$ term of HP $= a_{n} = \frac{1}{a + (n - 1) d}$ Option B is correct.

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