Using the index of a series as the domain and the value of the series as the range, is a series a function?

Question

Include the following in your answer:

Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series?
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric series?
Give real-life examples of both arithmetic and geometric sequences and series. Explain how these examples might affect you personally.

Yes, I would say your description constitutes a function.

And yes, the type of basic function can be determined by the type of series.