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Multiplication is repeated addition, so is there an explicit relation between arithmetic and geometric series if the first term is a and common difference d is equal to the common ratio q. Is it even possible to have such a case. This is not a textbook question,just something i am curious about.

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Instead of $ (a, d) $ I use $( P,n) $ in the same sense.

The amount of money A after n years follows Arithmetic Progression/series with rate of interest as per formula:

$ A = P( 1 + r\cdot n) $

The amount of money after n years follows Geometric Progression/series as per formula:

$ A = P( 1 + r^ n) $

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