# Comparing Sequences and Functions

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:

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

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

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

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#### Solution Preview

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

Every sequence is a function from set of natural numbers to the set containing the values of the sequence.

Arithmetic sequence:

If x is the first term and y is the common difference, then ...