Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function? Include the following in your answer: ? Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence? ? Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric sequence? ? Give at least two real-life examples of a sequences or series

An arithmetic sequence is a sequence created by adding a constant to the preceding term. An example is the odd numbers: 1, 3, 5, 7, ... which are formed by adding 2 to each term, starting with 1.
The general equation for an arithmetic sequence is:

where a1 is the first term, an is the nth term, and d is the difference between successive terms (e.g. d = 2 in the odd numbers example).
The question says to use the index of the sequence as the domain and the value of the sequence as the range. Here the domain is the list of n's (n = 1, 2, 3, ...) and the range is the an's (a1, a2, a3, ...). This is a function, and it corresponds to a line. See for yourself by graphing the odd numbers example: graph the points (1, 1), (2, 3), (3, 5), (4, 7). What is the slope of the line?

A geometric sequence is a sequence created by multiplying each preceding term by a constant. Take for example: 1, 3, 9, 27, ... which are formed by multiplying each term by 3, starting with 1.

The general equation for a geometric sequence is:

where a is a scale factor, an is the nth term, and r is the ratio between successive terms (our example has a = 1 and r = 3).

Again, the domain is the n's (n = 1, 2, 3, ...) and the range is the an's (a1, a2, a3, ...). This is similar to an exponential function. See this by substituting x for n and y for an in the geometric sequence: y = arx-1. Graph that function and see what it looks like.

Here are two examples of "real life" things that correspond to series/sequences. Which is arithmetic and which is geometric?

A bacterium divides every hour, so that at time 0, there is 1 bacterium, at 1 hour there are 2 bacteria, at 2 hours there are 4, at 3 hours there are 8, etc.

You look at the page numbers of only the right-hand pages of a book. These are 2, 4, 6, 8, etc.

please see the attached file.