Let a be the first term and r be the common ratio of a GP. ∴ Pth, Qth and Rth terms of a GP are respectively arP−1,arQ−1 and arR−1 According to question, arp−1=64.......(i) arQ−1=27....(ii) arR−1=36.......(iii) Dividing Eq. (i) by Eq. (ii), we get rp−Q=(
4
3
)3...(iv) Dividing Eq. (ii) by Eq. (iii), we get rQ−R=
3
4
⇒r3Q−3R=(
3
4
)3...(v) Multiplying Eq. (iv) and Eq. (v), we get rp−Q×r3Q−3R=1 ⇒rP−Q+3Q−3R=1 ⇒rP+2Q−3R=r0 ⇒P+2Q−3R=0 ⇒P+2Q=3R