Comparing Convergence Rates of Sequences

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SUMMARY

The discussion focuses on comparing the convergence rates of four numerical sequences: {32, 16, 8, 4, 2, 1}, {32, 16, 8, 2, 1, 0.5}, {32, 16, 4, 2, 1, 0.5}, and {32, 16, 4, 1, 0.25, 0.0625}. The primary goal is to determine which sequence converges the fastest by analyzing their rates of decrease. A mathematical formula is required to quantify the convergence rates, and the results should be visualized through plotting to facilitate comparison. The discussion emphasizes the importance of identifying the sequence that exhibits the steepest decline in values.

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onako
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I have the following sequences of numbers:
1) 32, 16, 8, 4, 2, 1
2) 32, 16, 8, 2, 1, 0.5
3) 32, 16, 4, 2, 1, 0.5,
4) 32, 16, 4, 1, 0.25, 0.0625

I'm interested which of the above has the fastest rate of convergence.
(mathematical formula is needed). I should be able to plot the rates of
convergence against each other, and it should be concluded from the plot.
(The data given above are just the illustration)
 
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This means I should be able to tell which sequence drops/decreases faster from the plot.
For example, given sequences {32, 16, 8, 4, 2, 1} and {128, 32, 8, 2, .5, .125} I should be able to tell that the second sequence drops faster (decreases by /4). How to extract this data and plot it, so that the answer is obvious? Thanks
 

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