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