Insert 7

Insert five harmonic means between 3 and 18

Correct answer:

a2 =  3.4839
a3 =  4.1538
a4 =  5.1429
a5 =  6.75
a6 =  9.8182

Step-by-step explanation:

a1=3 a7=18  b1=1/a1=1/3=130.3333 b7=1/a7=1/18=1180.0556 d=(b7b1)/(71)=(0.05560.3333)/(71)=51080.0463  b2=b1+d=0.3333+(0.0463)=311080.287  a2=1/b2=1/0.287=10831=31531=3.4839
b3=b2+d=0.287+(0.0463)=13540.2407 a3=1/b3=1/0.2407=5413=4213=4.1538
b4=b3+d=0.2407+(0.0463)=7360.1944 a4=1/b4=1/0.1944=367=517=5.1429
b5=b4+d=0.1944+(0.0463)=4270.1481 a5=1/b5=1/0.1481=274=634=6.75
b6=b5+d=0.1481+(0.0463)=111080.1019 a6=1/b6=1/0.1019=10811=99119.8182=9.8182   Verifying Solution:  B7=b6+d=0.1019+(0.0463)=1180.0556 A7=1/B7=1/0.0556=18

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