What Progression Do the AM, GM, and HM of 2 Numbers Form? #shorts

Consider two positive numbers a and b. Consider their arithmetic mean (AM), geometric mean (GM), and harmonic mean (HM). Then, what type of progression do these AM, GM, and HM form in this order?

#shorts #sequences #progressions #ArithmeticMean #GeometricMean #HarmonicMean

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[CornerstonesOfMath]

A quick side note: Conventionally, the common ratio (r) of the geometric progression is defined as

r = (n+1)th term / nth term

Therefore, if we consider a progression of AM, GM, HM in this exact order, then the ratio AM/GM = GM/HM given in the video must be

AM/GM = GM/HM = 1/r

instead of r.
The mathematical process shown in the video is still correct (as well as its conclusion), but I just wanted to clarify this.

[cloverisfan]

Does this work for more than 2 numbers