Another word for "average": the arithmetic mean of x1,...,xn is
(x1 + ... + xn) / n

A convex combination, the arithmetic mean is always somewhere between the largest and smallest elements.

In simpler terms, the arithmetic means are the terms between any nonconsecutive terms in an arithmetic sequence. You can determine arithmetic means between any number of terms in a sequence:

IE find four arithmetic means between -11 and 19 ...


The formula for any term n in an arithmetic sequence:
an=a1+(n-1)d
19=-11+(6-1)d
(19 is the first term, then there's four terms, plus the last term is six)
19=-11+5d
8=5d
d=5/8
start with 19 and then add 5/8 to 19, 5/8 to that sum (19 5/8), etc.

Not the most elegant math, but it works.

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