A Function:
Bob has worked for A company for 2 years. He got $100000 for his salary. Now his employer decides to raise his salary because of his ability. After arising, company pays him $5000 per month.

It is the function between the time(t) and money (f) he owns. f(t)=100000+5000t

A sequence:
A biology student is observing cell division. There is only one bacterium cell in a petri dish. Each second, one cell division occurs. After first division, two bacterium cells appear in the dish.
The sequence is n=1*2^(t-1)

A series:
A boss invests a really effective and risky task which monthly benefit is 1%. He spends $100,000,000 to invest initially. Because of the risk, after each month he takes 20% out of his investment(not include the benefit) to minimize the risk.

There is a series which is between time(t) and benefit(y).

Does the graph of your function have a horizontal asymptote?
No, because it is a linear function.
Does your sequence converge?
No, since it is a geometric sequence which has a common ratio of 2 being greater than 1.
Does your series converge?
Yes, it is a geometric series and the absolute value of r is smaller than 1.