IITJEE 2001
Algebra
Level
3
Let the positive numbers a,b,c,d be in A.P. Then abc,abd,acd,bcd are in
H.P(harmonic progression
G.P(Geometric progression)
A.P(Arithmetic progression
not in AP/GP/HP
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1 solution
Since a,b,c,d are in A.P.
a b c d a , a b c d b , a b c d c , a b c d d are in A.P.
b c d 1 , c d a 1 , a b d 1 , a b c 1 are in A.P.
bcd,cda,abd,abc are in H.P.
Hence, abc, abd,cda,bcd are in H . P