23. 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.

• @HRDARJI ,
  
  pls check.
  ur approach is correct but calculation and hence result is wrong.
  here d= -1/150
  and
  a= 3/50.
  
  Pls excuse me if there is any mistake on my part.
• 11 years agoHelpfull: Yes(11) No(1)
• if x1,x2,x3 are in hp
  so 1/x1,1/x2,1/x3 are in AP
  in ap series are a,a+d,a+2d+....
  given,
  7th term=1/50
  5th term=1/30
  i.e 1/30=a+4d....eq(1)
  1/50=a+6d....eq(2)
  solve eq(1)&(2)
  we get ,a=3/50
  d=-1/150
  4th term=a+3d=1/25
  6th term=a+5d=1/37.5
  so in differene is 37.5-25=12.5 ans
  
  
• 11 years agoHelpfull: Yes(11) No(0)
• 1/30 = a + 4d
  
  1/50 = a + 6d
  
  we get a=d= 1/150
  
  6th term =1/25
  4th term =1/37.5
  
  difference 37.5-25 = 12.5
• 11 years agoHelpfull: Yes(10) No(8)
• Hradarji has managed to match the answer with Engg skills.
  
  
  Actually a= 3/50 and d= -1/150 for AP formed by reciprocal of terms of HP series.
  
  The HP series will be
  150/9, 150/8,150/7,150/6,150/5,150/4,150/3,150/2,.....
  
  Diff between 6th and 4th term will be
  150/4-150/6 = 75/2-25 = 25/2=12.5
• 11 years agoHelpfull: Yes(3) No(0)
• @Hari priya..
  Hi,where did u get these questions, TCS new patterns?
• 11 years agoHelpfull: Yes(0) No(6)
• a7=1/50, a5=1/30 in AP....by solving it v cn calculate a=3/50 and d=-1/150...dn a4=2/50 nd a6=4/150......nw calculate d diff b/w 50/2 nd 150/4...i.e.12.5......s0, d)12.5 is d ans..
• 11 years agoHelpfull: Yes(0) No(0)