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

`r=5/2 or 2/5; 2/5, 1, 5/2 or 5/2, 1, 2/5`

Explanation

Let the three terms of the GP be `a/r, a` and `ar`. Then,
`a/rxxaxxar=1 rArr a^(3)=1 rArr a=1`.
So, the given terms are `1/r, 1` and r.
`:. 1/r+1+r=39/10 rArr r+1/r=(39/10-1)=29/10`
`rArr 10r^(2)+10=29r`
`rArr 10 r^(2)-29r +10=0`
`rArr (2r-5) (5r-2)=0`
`rArr r=5/2` or `r=2/5`
Hence, these terms are `2/5, 1, 5/2` or `5/2, 1, 2/5`.