ARITHMETIC AND GEOMETRIC PROGRESSIONS

ID# : 3538
Under Category : Science Mathematics
Source: www.thiel.edu

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In the arithmetic progression above, the first term is 2 and the common difference is 3. . We note that the average of all the terms of an arithmetic .

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in which each succeeding term is obtained by adding a fixed number to the preceding term iscalled an arithmetic progression. The general form of an arithmetic progression with n terms is therefore.. The average (or arithmetic mean) of n numbers is their sum divided by n. For example, the average of 1, 3, and 7 is 11/3. If each of the terms of a sum is replaced by the average of theterms, the sum is not altered. We note that the average of all the terms of an arithmeticprogression is the average of the first and last terms, and that the average is the middle term whenthe number of terms is odd, that is, whenever there is a middle term. If a is the average of r and s, then it can easily be seen that r, a, s are consecutive terms of an arithmetic progression. (The proof is left to the reader.) This is why the average is also calledthe arithmetic mean.

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