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 _________.

Let ar,a,ar be three terms in G.P.∴  Product of terms =a3=−1 (Given) ⇒ a=−1Now, sum of term =ar+a+ar=1312 (Given)⇒ −1r−1−r=1312or   12r2+25r+12=0or   (3r+4)(4r+3)=0or   r=−43,−34But r≠−43∴ |S|=a1−r=−11−−34=−11+34=−47=47