An arithmetic series is one where you add. A geometric series is one where you multiply. For example, if we start at 1 and add 2, we get 1,3,5,7,9,…, an arithmetic series (the odd numbers). If we start at 1 and *multiply* by 2, we get 1,2,4,8,16,…, a geometric series.
We can also talk about the arithmetic average of two numbers which is (x+y)/2, and the geometric average which is √(x×y).
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