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Average Groups

The nth term of a sequence is 2n + 3 for all counting numbers n. In terms of n, what is the arithmetic mean of a group of r terms with a median position of the rth term? For example, if r = 3, then examine the mean of the 2nd, 3rd, and 4th terms. If r = 5, then examine the mean of the 3rd, 4th, 5th, 6th, and 7th terms.

(Source: Adapted from Mathematics Teaching in the Middle School, May 1997)

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