Question 84139: Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function?
include in your answer:
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence?
Which 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 would effect you personally.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function?
Yes its a function. The definition of a sequence is a function in which the domain is only nonnegative integers
"Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence?"
the arithmetic sequence is most like a linear function. Remember, an arithmetic sequence is something like  while a linear function might look like  . Basically both functions are arithmetically increasing by a set number each time (in this case 2). There is a bigger difference between these two other than the variable difference. is a discrete function (only a certain set of numbers will work which means holes and gaps will occur) while is continuous (any number will work)
"Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric sequence? "
the geometric sequence is most like a exponential function. Remember, an geometric sequence is something like  while a exponential function might look like  . Basically both functions are doubling in value after each increase of a whole number and growing exponentially. Remember, these functions follow the same as above: the geometric sequence is discrete while the exponential function is continuous.
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.
Examples of arithmetic sequences: if you get paid $8 an hour then your paycheck would be based on the sequence  . So if you work 0 hours, then you get nothing. If you work 1 hour, you get 8 dollars; if you work 2 hours you get $16, etc.
Examples of geometric sequences: If you deposit $10,000 in a bank or CD ,which is compounded annually, at 10% interest, then your money will grow exponentially and will follow the geometric sequence  . So if you want to find out how much money you had at 3 years, simply plug in n=3 to see how much money you would have in your account.
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