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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 there are n harmonic means between 1 and 1/31 and the ratio of 7th and (n-1)th harmonic means is 9 : 5, then the value of n will be

•   12
•  13
•  14
•  15

14

Q2. If m is a root of the given equation (1-ab)x2 - (a2 + b2)x - (1+ab) = 0 and m harmonic means are inserted between a and b, then the difference between last and the first of the means equals

•  b-a
•  ab(b-a)
•  a(b-a)
•  ab(a-b)

ab(b-a)

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