## Properties of Harmonic Progression - Advance

In mathematics, a harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocals of an arithmetic progression. Equivalently, a sequence is a harmonic progression when each term is the harmonic mean of the neighboring terms.

Q1.  If b2, a2, c2 are in A.P., then a+c, b+c , c+a will be in

•  A.P.
•  G.P.
•  H.P.
•  None of these

H.P.

Q2.  If a, b, c, d be in H.P., then

•  a2 + c2 b2 + d 2
•  a2 + d2 > c2 + b2
•  ac + bd > b2 + c2
•  ac + bd > b2 + d2

ac + bd > b2 + c2

Q3.  If a1, a2, a3, ..... an are in H.P., then a1a2 + a2a3 + a3a4 + ........an-1an will be equal to

•   a1an
•  na1an
•  (n-1)a1an
•  None of these

(n-1)a1an

Q4.  If x, y, z are in H.P., then the value of expression log(x+z) + log(x-2y+z) will be

•  log(x-z)
•  2log(x-z)
•  3log(x-z)
•  4log(x-z)

2log(x-z)

Q6.  If (x+y)/2 , y , (y+z)/2 are in H.P., then x, y, z are in

•  A.P.
•  G.P.
•  H.P.
•  None of these

G.P.

Q6.  If a, b, c, d are in H.P., then

•  a+d>b+c
•  Both (a) and (b)
•  None of these

Both (a) and (b)

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