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=53≐1.6667 a6=5/11=511≐0.4545  b1=1/a1=1/1.6667=35=0.6 b6=1/a6=1/0.4545=115=2.2 d=(b6−b1)/(6−1)=(2.2−0.6)/(6−1)=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

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