Latest TCS Aptitude Question SOLUTION: 22. A sequence x1 , x2 and x3 …is said to be in a harmonic progression if the reciprocals 1/x1,1/x2 and 1/x3 are in arithmetic progression. The 5th term and the 7th term for an h

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22. A sequence x1 , x2 and x3 …is said to be in a harmonic progression if the reciprocals 1/x1,1/x2
and 1/x3 are in arithmetic progression. The 5th term and the 7th term for an harmonic progression are 30 and 50 respectively. What is the difference between the 6th and 4th term. a. 16
b. 14.5
c. 13.4
d. 12.5.

Asked In TCS Sankhadeep (11 years ago)

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Aritra Ray  (8 years ago)

30 & 50 are 5th & 7th term of H.P series
So, 1/30 & 1/50 are 5th & 7th term of A.P series
Let the 4th, 5th, 6th, 7th & 8th terms of A.P be a-2d, a-d, a, a+d, a+2d
Therefore, by the problem
a-d = 1/30
a+d = 1/50
now, 2d = (a+d) - (a-d)
= 1/50 - 1/30
= - 1/75
hence, d = -1/150
now, a-d = 1/30
so, a = 1/30 + d = 1/30 - 1/150 = 2/75
Therefore, 4th term of A.P = a - 2d = 3/75 = 1/25
6th term of A.P = a = 2/75 = 1/37.5
Hence, 4th term of H.P = 25
6th term of H.P = 37.5
Difference between them = (37.5 - 25) = 12.5

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Karthick Subramanian  (11 years ago)

diff b/w 1/30 and 1/30 is 1/75.
so series could be 2/75,1/30,1/25,1/50 (note tat the series started from 4th term to 7th)
so ans is 12.5

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Karthick Subramanian  (11 years ago)

ans 12.5 is right, but i made a typing mistake in 1st line
i.e diff of 1/30 and 1/50 is 1/75

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