is it true that AM>GM>HM only true for natural numbers? also can common ratio be negative?

Dear student,
This statement is not true.
As A.M>G.M>H.M is only true when numbers are positive and distinct real numbers.
but in general A.MG.MH.M for all positive real numbers.
here Equality holds only when two numbers are Equal.

As you were asking about that can common ratio be negative "YES"
Common ratio can be positive or negative but it cannot be zero.
Example 2,-4,8,-16,........is an G.P with common ratio -2.
hope i have cleared your doubt.
enjoy

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