Series/Sequence/Functions?

Question

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



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. One example should be arithmetic, and the second should be geometric. Explain how these examples would affect you personally.

Answer 1

An arithmetic sequence is a sequence with the difference between two consecutive terms constant. The difference is called the common difference.

A geometric sequence is a sequence with the ratio between two consecutive terms constant. This ratio is called the common ratio.
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(1) Domain based on "index" of sequence and Range based on "value"
As long as each "index" is not used to assign more than one "value" then it is a function. So I would say yes.
(2) arithmetic = linear
(3) geometric = exponential
(4) Geometric series - chain mail or pyramid scheme, multiplying each level by 2 or 10 more people, and adding up to calculate the total number of people connected
1 + 2 + 4 + 8 + 16 .....
Effect - you would quickly figure out that if you joined a sales club expecting to recruit more people under you, you would saturate the market and run out of people to contact not already involved

Arithmetic sequence - figuring out what days of the month you will be paid if you are paid each week (add 7) or every two weeks (add 14 days)
1, 15, 29
Effect - if you are trying to pay a bill by a certain date, you could find out if you will receive your next paycheck(s) in time