need help with sequences.?

Question

Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function?

I need to include this in my 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?

I also need :
two real-life examples of a sequences or series. One example arithmetic, and the second geometric. Explaining how they would affect someone personally. thank you for your help.

Answer 1

1/ Yes! Sequence is function of index.
2\ linear, as it looks like a+b*n (compare y=a+b*x)
3/ exponential, as it looks like a*b^n
4\ I had $20 at jan/01/2006, my income is $100 per month, the total sum at jan/01/2007 = 20+12*100, index being 12;
I put $200 into a bank with 2% profit monthly, I’ll have 200*(1+0.02)^12 bucks in a year, index being 12.

Answer 2

I guess a series could be classified as a function, an arithmetic sequence is like a linear function while a geometric sequence is more of an exponential function.

population growth, interest accumulation, radioactive decay etc. are examples. These are all I can come up with.
Hope this helps!

Answer 3

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