document.write( "Question 83722: Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function?\r
\n" ); document.write( "\n" ); document.write( "Include the following in your answer:
\n" ); document.write( "1. Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence?
\n" ); document.write( "2. Which one of the basic functions (linear, quadratic, rational, or exponential)is related to the geometric sequence?
\n" ); document.write( "3. Give at least two real-life examples of sequences or series. One example should be arithmetic, and the second should be geometic. Explain how these examples would affect you personally. The one thing I can think of is age, but I don't know how to put it correctly. \n" ); document.write( "

Algebra.Com's Answer #60326 by jim_thompson5910(35256) $\"\"$ $\"About$

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Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function? \r
\n" ); document.write( "\n" ); document.write( "Yes its a function. The definition of a sequence is a function in which the domain is only nonnegative integers\r
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\n" ); document.write( "\n" ); document.write( "\"Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence?\" \r
\n" ); document.write( "\n" ); document.write( "the arithmetic sequence is most like a linear function. Remember, an arithmetic sequence is something like $\"a%5Bn%5D=2n%2B1\"$ while a linear function might look like $\"f%28x%29=2x%2B1\"$ . 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. $\"a%5Bn%5D=2n%2B1\"$ is a discrete function (only a certain set of numbers will work which means holes and gaps will occur) while $\"f%28x%29=2x%2B1\"$ is continuous (any number will work)\r
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\n" ); document.write( "\n" ); document.write( "\"Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric sequence? \"\r
\n" ); document.write( "\n" ); document.write( "the geometric sequence is most like a exponential function. Remember, an geometric sequence is something like $\"a%5Bn%5D=2%5En\"$ while a exponential function might look like $\"f%28x%29=2%5Ex\"$ . 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.\r
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\n" ); document.write( "\n" ); document.write( "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.\r
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\n" ); document.write( "\n" ); document.write( "Examples of arithmetic sequences: if you get paid $8 an hour then your paycheck would be based on the sequence $\"a%5Bn%5D=8n\"$ . 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.\r
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\n" ); document.write( "\n" ); document.write( "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 $\"a%5Bn%5D=10000%281.1%29%5En\"$ . 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.\r
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