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.

• 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
  
• 9 years agoHelpfull: Yes(2) No(0)
• 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
• 12 years agoHelpfull: Yes(1) No(0)
• 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
• 12 years agoHelpfull: Yes(0) No(0)