`a`, `b`, `c`, `d` are in increasing `G.P.` If the `AM` between `a` and `b` is `6` and the `AM` between `c` and `d` is `54`, then the `AM` of `a` and `b` is

Options

A. `15`
B. `48`
C. `44`
D. `42`

Answer

D

Explanation

`(d)` Let `r` is the common ratio.
`implies(a+ar)/(2)=6` and `(ar^(2)+ar^(3))/(2)=54`
`impliesr^(2)=9impliesr=+-3impliesr=3(r ne -3)`
When `r=3`, `a=3, `AM` of `a` and `d=(a+ar^(3))/(2)=42`