Harmonic series

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

Correct answer:

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

Step-by-step explanation:

a1​=5/3=35​=132​≐1.6667 a6​=5/11=115​≐0.4545  b1​=1/a1​=1/1.6667=53​=0.6 b6​=1/a6​=1/0.4545=511​=251​=2.2 d=(b6​−b1​)/(6−1)=(2.2−0.6)/(6−1)=258​=0.32  b2​=b1​+d=0.6+0.32=2523​=0.92  a2​=1/b2​=1/0.92=1.087
b3​=b2​+d=0.92+0.32=2531​=1256​=1.24 a3​=1/b3​=1/1.24=0.8065
b4​=b3​+d=1.24+0.32=2539​=12514​=1.56 a4​=1/b4​=1/1.56=0.641
b5​=b4​+d=1.56+0.32=2547​=12522​=1.88 a5​=1/b5​=1/1.88=0.5319

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