## Chapter 8-9 Study Guide

1. Use sigma notation to write the given sum. Look at problems 1 - 4 in the chapter 9 review.*
2. Find the sum. Look at problems 5 - 8 in the chapter 9 review.*
3. Write the first five terms of an arithmetic sequence given two terms. Look at 15 - 18 in the chapter 9 review.*
4. Write the first five terms of a geometric sequence given two terms. Concentrate on example 5 in section 9.3 and problems of this nature. The difference being that this problem asks for the first five terms instead of a specific term.
5. Find the sum of an arithmetic series. You are given the first term and the last term and enough terms to figure out what the common difference is. You will need to find n, and then use the formula. An example of what this problem would look like is: 2 + 5 + 8 + ... + 23
6. Find the sum of a geometric series. Short and all terms are given for you. You could use the formula or digress and just add them together. Example: 9 + 3 + 1 + 1/3 + 1/9 + 1/27
7. Find the sum of an infinite geometric series written in sigma notation. Look at problems 9 and 10 in the chapter 9 review.
8. Use the binomial expansion theorem to expand a binomial. Look at problems 41 - 46 in the chapter 9 review.*
9. Find a specific term of a binomial expansion. Look at example 6 in section 9.5.
10. Multiply two matrices.
11. Multiply a scalar and a matrix.
12. Find the transpose of a matrix.
13. Find the determinant of a 2x2 matrix.
14. Use Cramer's Rule to solve a 2x2 system of linear equations. No credit will be given if you don't use Cramer's Rule.
15. Find the determinant of a 3x3 matrix (if you know the shortcuts, this is really easy)
16. Find the inverse of a 3x3 matrix (again, much easier than it could be).
17. Find the sum of a 3x3 matrix with it's transpose.
18. Solve a 2x2 system of equations using Gauss-Jordan elimination. No credit will be given if you don't use Gauss-Jordan elimination. You don't have to pivot (please do, though), but you have to use Gauss-Jordan elimination.
19. Use mathematical induction to prove a given formula. Study the text (not the exercises) of section 9.4.*
20. Use mathematical induction to prove a given formula. Look at problems 21 - 24 in the chapter 9 review.*
Problems denoted with a * are directly from the problems I asked you to look at. It might be even or odd.