If 5th, 8th, and 11th terms of a G.P. are `p ,\ q\ a n d\ s` respectively, prove that `q^2=p sdot`

Options

A. `p^(2)=q^(2)+r^(2)`
B. `q^(2)=pr`
C. `p^(2)=qr`
D. pqr+pq+1=0

Answer

B

Explanation

Let A be the first term and R be the common ratio of the G.P. Then,
`p=AR^(3),q=AR^(6)andr=AR^(9)`
Clearly,
`(AR^(6))^(2)=(AR^(3))(AR^(9))rArrq^(2)=prrArrprrArrp,q,r` are in G.P.
ALITER If the terms of a G.P. are chosen at regular intervals, they also form a G.P.