Arithmetic Terms of Sequences and Series

1) How do I use the arithmetic sequence of numbers 1, 3, 5, 7, 9,...to find the following:
a) What is d, the difference between any 2 terms?
b) I don't have a clue how to solve this one. Using the formula for the nth term of an arithmetic sequence, what is 101st term?
c) Another difficult problem. Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?
d) Using the formula for the sum of an arithmetic series, how do I find out what is the sum of the first 30 terms?
e) How do I find out what observation can be made about the sums of this series (The hint given is: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)?

2) Please assist me in using the geometric sequence of numbers 1, 2, 4, 8,...to find the following:
a) What is r, the ratio between 2 consecutive terms?
b) Using the formula for the nth term of a geometric sequence, how do I find out what is the 24th term?
c) Using the formula for the sum of a geometric series, how do I find out what is the sum of the first 10 terms?

3) Using the geometric sequence of numbers 1, 1/2, 1/4, 1/8,...to find the following:
a) What is r, the ratio between 2 consecutive terms?
b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Round the answer to 4 decimals.
c) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Round the answer to 4 decimals.
d) What observation can be made about these sums? In particular, what number does it appear that the sum will always be smaller than?

4) CLASSIC PROBLEM - A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Brown came out and gratefully thanked the traveling salesman for saving his daughter's life. Mr. Brown insisted on giving the man an award for his heroism.

So, the salesman said, "If you insist, I do not want much. Get your checkerboard and place one penny on the first square. Then place two pennies on the next square. Then place four pennies on the third square. Continue this until all 64 squares are covered with pennies." As he'd been saving pennies for over 25 years, Mr. Brown did not consider this much of an award, but soon realized he made a miscalculation on the amount of money involved.
a) How much money would Mr. Brown have to put on the 32nd square?
b) Could you assist me in figuring out how much would the traveling salesman receive if the checkerboard only had 32 squares?
c) How do I calculate the amount of money necessary to fill the whole checkerboard (64 squares). How much money would the farmer need to give the salesman?

5) Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function?
I have to include the following in my answer: Can you assist?
- 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?
- 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.