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.

Create a free account to view solution

View Solution Free
Topic: Progression (Sequence and Series)·Practice all Progression (Sequence and Series) questions

More Progression (Sequence and Series) Questions

If the sum of four numbers in A.P. be 48 and that the product of the extremes to the means is product of 27 to 48 then t...Let a1,a2 , ......a10 in AP and h1, h2, ...... h10 be in HP. If a1 = h1 = 2 and a10 = h10 = 3, then a4h7 is...If the product of three terms of G.P. is 512. If 8 added to first and 6 added to second term, so that number may be in A...The change in the value of g at a height ′h′ above the surface of the earth is the same as at a depth &#8242...Given two numbers a and b, let A denotes the single A.M. and S denote the sum of n A.M.′s between a and b, then S/...