Insert four number between 6 and 192 so that the resulting sequence is a G.P.

Explanation

Let ` G_(1), G_(2), G_(3) G_(4)` be the four G.M.'s
Here ` a = (8)/(27) and b = (-81)/(16)`
` r = ((b)/(a))^((1)/(n+1))=(((-81)/(16))/((8)/(27)))^((1)/(7)) = (( -81)/(16) xx (27)/(8))^((1)/(7)) = ((-3)/(2))^(7xx(1)/(7)) = (-3)/(2)`
`G_(1) = ar = (8)/(27) xx ((-3)/(2)) = (-4)/(9)`
` G_(2) = ar^(2) = (8)/(27) xx (9)/(4) = (2)/(3)`
` G_(3) = ar^(3) = (8)/(27) xx ((-27)/(8)) = - 1`
` G_(4) ar^(4) = (8)/(27) xx ((81)/(16)) = (3)/(2)`
` G_(5) = ar^(5) = (-9)/(4)`
` G_(6) = ar^(6) = (27)/(8)` .