Question 1185584: Find the missing term in harmonic sequence. Show the solution
___,1/2,2/5,1/3,___
Answer by greenestamps(13209)   (Show Source):
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In a harmonic sequence, the reciprocals of the terms form an arithmetic sequence.
Given sequence: ___, 1/2, 2/5, 1/3, ___
Reciprocals: ___, 2, 5/2, 3, ___
The common difference in the sequence of reciprocals is 1/2; fill in the blanks: 3/2, 2, 5/2, 3, 7/2
The completed harmonic sequence: 2/3, 1/2, 2/5, 1/3, 2/7
Note the pattern in the harmonic sequence is easier to see if we write the terms with a common numerator: 2/3, 2/4, 2/5, 2/6, 2/7
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