Find 3 geometric means between 10 and 160.

Options

A. 20, 40, 80
B. 20, 60, 100
C. 30, 60, 90
D. None of these

Answer

A

Explanation

`"Let "G_(1),G_(2),G_(3), "be three geometric means between 10 and 160."`
`therefore" "10,G_(1),G_(2),G_(3), 160 " are in G.P."`
`"and "T_(5)=160`
`rArr" "10cdotr^(4)=160`
`rArr" "r^(4)=16`
`rArr" "r=pm12`
If r=2, then
`G_(1)=10xx2=20`
`G_(2)=20xx2=40`
`G_(3)=40xx2=80`
If r=-2, then
`G_(1)=10xx(-2)=-20`
`G_(2)=-20xx(-2)=40`
`G_(3)=40xx(-2)=-80`
`therefore" Required G.M.'s 20, 40, 80, or -20, 40, -80."`