Question

The sum of first three terms of a GP is 39/10 and thier product is 1 . find the common ratio and the terms

Answer 1

Dear Student,

Let the three terms of gp are a/r, a , ar.
Therfore , a/r x a x ar = 1.
So, a³ = 1
a = 1
As sum of all three terms =39/10
So, a/r + a + ar = 39/10
1/r + 1 + r = 39/10
1 + r + r² = 39 /10

10 + 10r + 10r² = 39
10r² - 29r + 10 = 0
10r² - 25r -4r + 10 = 0
5r(2r - 5) - 2(2r - 5) = 0
( 5r - 2) ( 2r - 5 ) = 0
So r = 2/5 or 5/2
Hence the three no. are :-
When r = 2/5
a/r , a , ar = 5/2 , 1 ,2/5 ......(1)
When r = 5/2
a/r , a , ar = 2/5, 1 ,5/2 ......(2)
From eq (1) & (2)
The three numbers are
5/2 , 1 , 2/5 or 2/5 , 1, 5/2

Regards