Progression (Sequence and Series)Hard

Question

If x > 1, y > 1, z > 1 are in GP, thenare in

Options

A.AP
B.HP
C.GP
D.None of these

Solution

Let the common ratio of the GP be r. Then,
        y = xr and z = xr2
⇒     ln x + ln r and ln z = x + 2ln r
Let   A = 1 + ln x, D = ln r
Then,    
       
and  
Therefore, are in HP.

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