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# Arithmetic and Geometric Series Sequences

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Using the index "n" of the partial sums of a series as the domain, and the value of the corresponding partial sums of the series "Sn" as the range, is a series a function?

- Which of the basic functions, (i.e. - linear, quadratic, rational, exponential), is related to the arithmetic series?
- Which of the basic functions, (i.e. - linear, quadratic, rational, exponential), is related to the geometric series?

Give a couple of real life examples of both the Arithmetic and Geometric sequences and series. Also, explain how these types of examples might affect you personally.

https://brainmass.com/math/algebra/arithmetic-geometric-series-sequences-135655

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Yes, it is a function by using the index of a sequence as the domain and the value of the sequence as the range. Each of the input, i.e. the index, is corresponding to exact one output, the value of the sequence.

For an arithmetic sequence, a_n = a_1 + (n - 1) d, where a_1 is the first value of the sequence, d is the common difference of successive members, and n is the index. So it is a linear relationship between the index and the value with fixed and d.

For the geometric sequence, a_n = a_1 * r^(n-1) , , where a_1 is the first value of the sequence, r is common ratio of successive members, and n the index. So it is an exponential function.

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