Let the first three terms of G.P. be

a

r

, a , ar , where a is the first term and r is the common ratio.
Then

a

r

+ a + ar =

39

10

and

a

r

× a × ar = 1
⇒ a(

1

r

+1+1) =

39

10

and a3 = 1 ⇒ a = 1
∴ 1(

1

r

+1+r) =

39

10

⇒ 10 (1 + r + r2) = 39r ⇒ 10r2 – 29r + 10 = 0
⇒ 10r2 – 25r – 4r + 10 = 0 ⇒ (5r – 2) (2r – 5) = 0
⇒ r =

2

5

,

5

2

(i) When r =

5

2

, the terms are

2

5

,1,

5

2

(ii) When r =

2

5

, then terms are

5

2

,1,

2

5