Question 53287: 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. One example should be arithmetic, and the second should be geometric. Explain how these examples would affect you.
Answer by Nate(3500)   (Show Source):
You can put this solution on YOUR website! Arithmetic Sequence can look like this: 0,2,4,6,8,10....x + 2
Simply, you add two each time. Relatively, you just add a basic constant.
This can be seen in a linear line as: y = 2x + 0
A linear line shows that after  values there are the constant times that value for .
Geometric Sequence can look like this: 1,3,9,27,81,243....3^x
Simply, you just multiply by three eacch time.
Think about this:
for 0 values ~> 3^0 = 1
for 1 value ~> 3^1 = 3
for 2 values ~> 3*3 = 9
Of course, this looks like: y = 3^x
Geometric sequence looks like an exponential function.
Example:
Arithmetic: If you develop two bumps a day, how many bumps would you have in a week?! Explains that you should check a docter....
Geometric: Bouncing of a ball may be decided as 1/3 of the previous bounce. This could better help you understand physics. Will the ball bounce forever? Mathematically, yes! Realistically, no!
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