If `p^(th), q^(th), r^(th) and s^(th)` terms of an A.P. are in G.P, then show that (p – q), (q – r), (r – s) are also in G.P.

Options

A. A.P
B. G.P
C. H.P
D. none of these

Answer

B

Explanation

Given that
a+(p-1)d=A
a+(q-1)d=AR
`a+(r-1)d=AR^(2)`
`a+(s-1)d=AR^(3)`
where R is common ratio of G.P. Now,
`p-q=(A-AR)/d,q-r=R((A-AR)/d)`
Clearly,p-q,q-r,r-s are in G.P.