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

Given: Sum of first three terms of a G.P. is and their product is 1

Let , a , r be the three terms in G.P.

and

⇒ a³ = 1

⇒ a = 1

_{Substitute ‘a’ in –1, we get}

+ 1 + r =

_{⇒ 10 × (1 + r + r}²) = 39 × r

_{⇒ 10 +10 × r + 10 × r}² = 39 × r

_{⇒ 10r}² + 10r – 39r + 10 = 0

_{⇒ 10r}² - 29r + 10 = 0

_{⇒ 10r}² -25r – 4r + 10 = 0

_{⇒ 5r(2r – 5) -2(2r – 5) = 0}

_{⇒ (5r-2)(2r-5) = 0}

⇒ r =

∴ The three terms in the G.P. are