Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a functi
Posted on Jun 27, 2008 under domain news and reports | 4 CommentsInclude 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. One example should be arithmetic, and the second should be geometric. Explain how these examples would affect you personally
June 27th, 2008 at 10:34 am
first example: my brain just exploded
second example: right now blood is gushing out of every orafice on my body
something for you to think about: The mind actually acts like a hologram.
June 27th, 2008 at 10:34 am
Since any mapping from one space to another can be considered a function, then a sequence could be called a function. It doesn't matter whether the sequence is arithmetic (e.g. 1, 2, 3, 4, 5, … — i.e., linear) or geometric (e.g. 1, 1.5, 2.25, 3.375, … — i.e., exponential). And, do any of these affect me personally? No.
June 27th, 2008 at 10:34 am
Sounds something like a question right out of a textbook. To answer your question, yes, if you consider the index of a sequence as the domain and the value of the sequence as the range, the sequence can be considered as a function (in fact, we consider these things in calculus but with series rather). It definitely won't be a continuous function but it will be a function.
As for your other requirements, just look at the closed form (explicit formula) for the sequence. Whatever it looks like, that's the kind of function it will be. An arithemtic sequence's closed form looks like an equation for a line, therefore it can be considered as a linear function. A geometric sequence has the same form as a power (exponential) function.
Now, I am not going to do ALL the work for you so you think of real-life examples that you need.
October 30th, 2011 at 2:02 pm
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