Question 83819
<font color="blue">Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function?</font> 

Yes its a function. The definition of a sequence is a function in which the domain is only nonnegative integers


<font color="blue">"Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence?" </font>

the arithmetic sequence is most like a linear function. Remember, an arithmetic sequence is something like {{{a[n]=2n+1}}} while a linear function might look like {{{f(x)=2x+1}}}. 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[n]=2n+1}}} is a discrete function (only a certain set of numbers will work which means holes and gaps will occur) while {{{f(x)=2x+1}}} is continuous (any number will work)



<font color="blue">"Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric sequence? "</font>

the geometric sequence is most like a exponential function. Remember, an geometric sequence is something like {{{a[n]=2^n}}} while a exponential function might look like {{{f(x)=2^x}}}. 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.


<font color="blue">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.</font>


Examples of arithmetic sequences: if you get paid $8 an hour then your paycheck would be based on the sequence {{{a[n]=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.


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[n]=10000(1.1)^n}}}. 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.