Insert four

Insert four harmonic means between 3/7 and 3/19

Correct answer:

a2 =  0.3191
a3 =  0.2542
a4 =  0.2113
a5 =  0.1807

Step-by-step explanation:

a1​=3/7=73​≐0.4286 a6​=3/19=193​≐0.1579  b1​=1/a1​=1/0.4286=37​=231​≐2.3333 b6​=1/a6​=1/0.1579=319​=631​≐6.3333 d=(b6​−b1​)/(6−1)=(6.3333−2.3333)/(6−1)=54​=0.8  b2​=b1​+d=2.3333+0.8=1547​=3152​≐3.1333  a2​=1/b2​=1/3.1333=4715​=0.3191
b3​=b2​+d=3.1333+0.8=1559​=31514​≐3.9333 a3​=1/b3​=1/3.9333=5915​=0.2542
b4​=b3​+d=3.9333+0.8=1571​=41511​≐4.7333 a4​=1/b4​=1/4.7333=7115​=0.2113
b5​=b4​+d=4.7333+0.8=1583​=5158​≐5.5333 a5​=1/b5​=1/5.5333=8315​=0.1807

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Showing 2 comments:
Shells52
a6 should be 3/19 not 4/19

Dr Math
thank you, we corrected a solution.





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