Harmonic series

Insert four members between 5/3 and 5/11 to form harmonic series (means).

Correct result:

a2 =  1.087
a3 =  0.8065
a4 =  0.641
a5 =  0.5319

Solution:

a1=5/3=531.6667 a6=5/11=5110.4545  b1=1/a1=1/1.6667=35=0.6 b6=1/a6=1/0.4545=115=2.2 d=(b6b1)/(61)=(2.20.6)/(61)=825=0.32  b2=b1+d=0.6+0.32=2325=0.92   a2=1/b2=1/0.92=2523=1.087
b3=b2+d=0.92+0.32=3125=1.24 a3=1/b3=1/1.24=2531=0.8065
b4=b3+d=1.24+0.32=3925=1.56 a4=1/b4=1/1.56=2539=0.641
b5=b4+d=1.56+0.32=4725=1.88 a5=1/b5=1/1.88=2547=0.5319



We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
avatar




Tips to related online calculators
Looking for calculator of harmonic mean?
Looking for a statistical calculator?

You need to know the following knowledge to solve this word math problem:

Next similar math problems:

  • Insert 7
    seq_1 Insert five harmonic means between 3 and 18
  • Insert 6
    seq Insert four harmonic means between 3/7 and 3/19
  • Insert 3
    arithmet_seq Insert five arithmetic progression members between -7 and 3/2.
  • Insert 5
    sequence_geo_1 Insert five harmonic means between 1/2 and 1/26
  • Harmonic mean
    means_math If x, y, z form a harmonic progression, then y is the harmonic mean of x and z. Find the harmonic mean of the numbers 6 and 5.
  • Insert 4
    arithmet_seq_1 Insert 3 arithmetic means between 3 and 63.
  • HP - harmonic progression 2
    seq Compute the 16th term of the HP if the 6th and 11th term of the harmonic progression are 10 and 18 respectively.
  • Insert AP member
    mean_normal Insert arithmetic means between 75 and 180.
  • HP - harmonic progression
    sequence_geo_1 Determine the 8th term of the harmonic progression 2, 4/3, 1,…
  • HP - harmonic progression
    exp_growth_1 Determine the 10th term of the harmonic progression 6,4,3,…
  • Sequence 11
    sequence_geo_2 What is the nth term of this sequence 1,1/2,1/3,1/4,1/5 ?
  • Sequence 3
    75 Write the first 5 members of an arithmetic sequence: a4=-35, a11=-105.
  • Insert into GP
    archimedes_1 Between numbers 5 and 640 insert as many numbers to form geometric progression so sum of the numbers you entered will be 630. How many numbers you must insert?
  • Negative difference
    arithmet_seq Find four arithmetic progression members between 7 and -6.
  • Sum of series
    question Determine the 6-th member and the sum of a geometric series: 5-4/1+16/5-64/25+256/125-1024/625+....
  • Harmonic and arithmetic means
    Plot_harmonic_mean The local Utah Department of Child Service office wants to project staffing needs based on current social worker assignments. They have the number of cases per social worker for the following staff: Mary: 25 John: 35 Ted: 15 Lisa: 45 Anna: 20 Calculate: a
  • Harmonic mean
    sequence_geo Harmonic means of 6 and 12