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# series is a function with index as independent variable

UNIT FIVE DB B:
Using the index of a series as the domain and the value of the series as the range, is a series a function?
? 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.

Discussion Board Questions (my hints in bold)

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

For example, if you have sequence : 2,5,8,11,.... Your index is the term number and the value of the sequence is the range. For this example:

Domain (term number) Range (value of term)
1 2
2 5
3 8
4 11

Graph some of these and decide if it is a function (remember to look back to unit one to see what makes a function!)

? Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence?

. EXPLAIN YOUR ANSWER. You do not need to include the graph unless you want to, but explain why it is the graph that you have chosen!

? Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric sequence?

EXPLAIN YOUR ANSWER. You do not need to include the graph unless you want to, but explain why it is the graph which you have chosen!

? Give at least two real-life examples of a sequences or series. One example should be arithmetic, and the second should be geometric. Explain how these examples would affect you personally.

Go to Google and type in "applications for geometric or arithmetic sequences", go to one of the websites listed at the end of the multimedia presentation, look through the book, or be creative and make up your own real life example A) give the application problem for an arithmetic sequence, include what makes it arithmetic!! B) give an application problem for a geometric problem and include what makes it geometric. Give as much information as you can about your examples. You don't need to explain how these examples might effect you personally unless you want to, but make sure that you explain what makes your example geometric or arithmetic!

#### Solution Preview

Pleas see the detailed solution in the attached WORD file.

Yes, it is a function by using the index of a sequence as the domain and the value of the sequence as the range. ...

#### Solution Summary

The solution explains the definition of the function. It explains the type of the functions that the arithmetic and geometric series belong to using the index as the independent variable and the value of the series as the range. It also includes real life applications of the sequences.

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