Question

2) Find the 10th term of the Harmonic progression,

1/2,1/4,1/6............. 10th term
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Answer 1

Answer:  1/20

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Explanation:

The denominators 2, 4, 6, ... are in an arithmetic progression

• first term = 2
• common difference = 2

We have the multiples of 2.

• first denominator = 1*2 = 2
• second denominator = 2*2 = 4
• third denominator = 3*2 = 6

And so on.

The tenth denominator is 10*2 = 20

Therefore, the tenth term of the harmonic progression is 1/20

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Side note:

An arithmetic progression is of the form $a, a+d, a+2d, a+3d, \ldots$

A harmonic progression is of the form $\frac{1}{a}, \frac{1}{a+d}, \frac{1}{a+2d}, \frac{1}{a+3d}, \ldots$

I.e. take the reciprocal of the arithmetic sequence to get the harmonic sequence, or vice versa.