Question

The sum of first three terms of a gp is 39/10 and their product is 1.find common ratio

Answer 1

Answer:

let the first three terms of a gp series are a/r,a,ar

here r is the common ratio

so,

a/r.a.ar=1

a^3=1

a=1

again,

a/r+a+ar=39/10

putting a=1,

1/r+1+r=39/10

1/r+r=39/10-1=29/10

(1+r^2)/r=29/10

10r^2+10=29r

10r^2-29r+10=0

10r^2-25r-4r+10=0

5r(2r-5)-2(2r-5)=0

(2r-5)(5r-2)=0

2r-5=0. 5r-2=0,5r=2,r=2/5

2r=5

r=5/2

so the common ratio is 5/2 or 2/5