The sum of first three terms of a G.P. is `(39)/(10)` and their product is 1. Find the common ratio and the terms.

Answer

N/a

Explanation

Let three terms of G.P. be `(a)/(r)`, a and ar.
Then product of terms `=(a)/(r)xxaxxar=a^(3)`
`therefore" "a^(3)=1impliesa=1`
and `(a)/(r)+a+ar=(39)/(10)`
`(1)/(r)+1+r=(39)/(10)" " (:. a=1)`
`implies (1+r+r^(2))/(r)=(39)/(10)`
`implies10+10r+10r^(2)=39r`
`implies10r^(2)-29r+10=0`
`implies10r^(2)-25r-4f+10=0`
`implies5r(2r-5)-2(2r-5)=0`
`implies(5r-2)(2r-5)=0`
`impliesr=(2)/(5) or r=(5)/(2)`
If `r=(2)/(5)` the terms `(1)/(2//5)1,1*((2)/(5))-=(5)/(2),1,(2)/(5)`
If `r=(5)/(2)` then terms `(1)/(5//2),1,*((5)/(2))-=(2)/(5),1,(5)/(2)`
Therefore, common ratio`=(2)/(5) or (5)/(2)` and three terms of G.P are `(5)/(2),1,(2)/(5) or (2)/(5),1,(5)/(2)`