A sequence x1,x2,x3…. Is said to be in harmonic progression if the reciprocals 1/x1,1/x2,1/x3… are in arithmetic progression. The 5th and 7th term for harmonic progression are 30 and 50 respectively what is difference between 6th and 4th term ?

• hp series is
  a,a/1+d,a/1+2d,.........
  
  so applying this
  5th term is 30=a/1+4d
  
  and 7th term is 50=a/1+6d
  
  so from this two eq. we get
  
  a=50/3
  and d=-1/9
  
  putting this two for 4th and 6th term we get 4th term =25 ..6th term=37.5
  difference=12.5ans....
• 11 years agoHelpfull: Yes(36) No(1)
• for harmonic series a,a/1+d,a/1+2d,a/1+3d.....
  so for 5th term 30=a/1+4
  a=150....
  for 6th term =150/1+5=25
  4th term =150/1+3=37.5
  difference=37.5-25=12.5
• 11 years agoHelpfull: Yes(30) No(9)
• series of alternate terms hp or ap is also an hp or ap
  so the difference will be same but opposite sign as in the given question the required different is reverse
  20 ans.
• 11 years agoHelpfull: Yes(1) No(15)