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a, b, c, d are in increasing G.P. If the...

`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 `d` is

A

`15`

B

`48`

C

`44`

D

`42`

Text Solution

Verified by Experts

The correct Answer is:
D
`(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`
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