The sum of first three terms of a G.P. is and their product is 1. Find the common ratio and the terms.

Their product = = 1

or a³ = 1

or a = 1

Again =

or =

or = r

or 1 + 10r + 10r² = 39r

or 10r² - 29r + 10

or 10r² - 25r – 4r + 10 = 0

or 5r(2r – 5) – 2(2r – 5) = 0

or (2r – 5) (5r – 5) = 0

or r =

Case (i) When r =

Numbers are

Case (ii) When r =

Numbers are

or or

Hence three numbers are or