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

Let the first three terms of G.P. be

It is given that

⇒

⇒ a = 1

And

⇒

⇒ …(a = 1)

⇒

⇒ 10(1 + r²) = 29r

⇒ 10r² - 29r + 10 = 0

⇒ 10r² - 25r - 4r + 10 = 0

⇒ 5r(2r - 5) - 2(2r - 5) = 0

⇒ (2r - 5)(5r - 2) = 0

⇒ r =

Therefore the first three terms are:

i)if r = then

ii)if r = then

Ans:Common ratio r = and the first three terms are:

i)if r = then

ii)if r = then