Let the sum of first three terms of G.P. with real terms be 13/12 and their product is -1. If the absolute value of the sum of their infinite terms is `S ,` then the value of `7S` is ______.

Answer

4

Explanation

Let `a/r`,a,ar be the three tems in G.P.
`therefore` Product of terms=`a^(3)`=-1 (Given)
`rArra=-1`
Now, sum of terms `=a/r+a+ar=13/12` (Given)
`rArr(-1)/r-1-r=13/12`
or `12r^(2)+25r+12=0`
or `(3r+4)(4r+3)=0`
or `r=(-4)/3,(-3)/4`
But `rne(-4)/3`
`thereforeabsS=abs(a/(1-r))=abs((-1)/(1-((-3)/4)))=abs((-1)/(1+3/4))`
`=abs((-4)/7)=4/7`