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If pth, qth , rth and sth terms of an AP...

If pth, qth , rth and sth terms of an AP are in GP then show that (p-q), (q-r), (r-s) are also in GP

A

A.P

B

G.P

C

H.P

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
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.
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