Question

The sum of first three terms of a geometric progression is 39/10 and their product is 1. Find the common ratio and the terms.

Answer 1

Let the 3 term in GP are a/r a and ar

Qudratic equation 

∴ 10r² – 25r – 4r + 10 

⇒ 50(2r – 5) -2 (2r – 5) = 0 

(2r – 5) = 0 or 5r – 2 = 0

∴ r = 5/2 or r = 2/5

∴ the three terms are 

at a = 1, r = 5/2

I term a/r = 1/(5/2) = 2/5

II term a = 1 

III term a_r = 5/2

at a = 1, r = 2/5

I term a_r = 2/5

II term a = 1 

III term = 2/5