1. Suppose you buy a new car for $18,000. At the end of n years, the value of your car is given by the sequence vn = 18000(3/4)n, n = 1, 2, 3, …..Find the fifth term and explain what this value represents. Describe the nth term of the sequence in terms of the value of your car at the end of each year.
2. Suppose you have the following recursion formula a1 = 1, a1 = 2, and an = (an-1) +
(an-2) for integers n ≥ 3. How would you determine the next three terms?
3. Given any sequence, how can you determine if it is an arithmetic sequence?
4. Suppose you are provided with an arithmetic sequence. How can you find the sum of n terms of the sequence without having to add all of the terms?
5. Given any sequence, how can you determine if it is a geometric sequence?
6. Suppose you are provided with a geometric sequence. How can you find the sum of n terms of the sequence without having to add all of the terms?
7. Suppose a rumor is spread by first one person telling another individual and then the individual telling two other people. Each person in turn tells two other people. Can you consider this an arithmetic or geometric sequence? Explain your answer.
8. Suppose Javier invests $150 every 3 months into an account that pays 4% annual interest compounded quarterly. Provide a list of the account balance for the first 4 quarters. Is this an example of an arithmetic or geometric sequence?
