The sum of first three terms of a GP is 39 10 and their product is 1 . Find the common ratio and these three terms.

Let the first three terms of G.P. be a r , a , a r It is given that a r × a × a r = 1 ⇒ a 3 = 1 ⇒ a = 1 And a r + a + a r = 39 10 ⇒ a 1 r + 1 + r = 39 10 ⇒ 1 r + 1 + r = 39 10 … ( a = 1 ) ⇒ 1 r + r = 39 10 - 1 = 29 10 ⇒ 10 1 + r 2 = 29 r ⇒ 10 r 2 - 29 r + 10 = 0 ⇒ 10 r 2 - 25 r - 4 r + 10 = 0 ⇒ 5 r ( 2 r - 5 ) - 2 ( 2 r - 5 ) = 0 ⇒ ( 2 r - 5 ) ( 5 r - 2 ) = 0 ⇒ r = 5 2 · 2 5 Therefore the first three terms are: i ) If r = 5 2 then 2 5 , 1 , 5 2 ii ) If r = 2 5 then the terms are 5 2 , 1 , 2 5