Using the index "n" of the partial sums of a series as the domain, and the value of the corresponding partial

Question

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?

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.

Answer 1

1)Yes,it is a function as for each n you have always a corresponding Sn
The partial sums of an arithmetic seriesSn= na1+(n-1)*n*r/2 which is a quadratic function of n
The partial sums of a geometric series Sn=a1(r^n-1)/(r-1) is an exponential function of n
Your age is an arithmetic sequence
The amount of a bank account compounded yearly is geometric sequence
An=(1+r)^n where r is the yearly interest in per one (6%=0.06)