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if x> 1, y> 1, z> 1 are in G.P , then  \frac{1}{1+logx},\frac{1}{1+logy},\frac{1}{1+logz} are in

  • Option 1)

    A.P

  • Option 2)

    H.P

  • Option 3)

    G.P

  • Option 4)

    None of these

 

Answers (1)

best_answer

As learnt in

Harmonic Progression (HP) -

The sequence a_{1},a_{2},-------a_{n},

Where a_{1}\neq 0 for each is an HP, if the sequence  \frac{1}{a_{1}},\frac{1}{a_{2}}-----\frac{1}{a_{n}}

is an AP

- wherein

eg \frac{1}{2},\frac{1}{5},\frac{1}{8},\frac{1}{11}----

 

 If x, y, z are in G.P.

then log x, log y, log z are in A.P.

Thus, \frac{1}{1+logx}, \frac{1}{1+logy}, \frac{1}{1+logz} are in H.P.

 


Option 1)

A.P

This solution is incorrect

Option 2)

H.P

This solution is correct

Option 3)

G.P

This solution is incorrect

Option 4)

None of these

This solution is incorrect

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