# Study Guide - Chapter 9

## Math 116

- Write the first five terms of an arithmetic sequence. Two parts. Given the first term and the
common difference for one part and two terms for the second part.
- Write the first five terms of a geometric sequence. Two parts. Given the first term and the
common difference for one part and two terms for the second part.
- Find the general term of a geometric sequence. Find the sum of a geometric sequence. Two
parts.
- Find the general term of an arithmetic sequence. Find the sum of an arithmetic sequence. Two
parts.
- Mathematical induction. Two parts.
- Find the closed form for a summation. Write it in factored form.
- Find a combination, permutation, and factorial. Three parts.
- Find a specific term in the binomial expansion.
- Expand a binomial using the Binomial Expansion theorem.
- Simplify the ratio of two factorials.
- Find the sum of an infinite geometric sequence.
- Compute the number of ways a certain event can be accomplished. These could be
combinations, permutations, distinguishable permutations, or the fundamental counting
principal. Three parts. Sentence problems.

Question 5 is worth 10 points per part. All other problems are worth 4 points per part.

### Notes on Mathematical Induction problems

The two mathematical induction problems are directly from the textbook. This can not be said
about problems on the test in general. Look at problems 15 - 25 (odd and even) in section 9.4.
Realize that I will be grading the work in the Mathematical Induction problems, not the final
answer.

Here is the breakdown of points: 1 point each for writing the three *correct* steps down (Show
n=1 is wrong). 1 point for showing true for n=1, 1 point for correctly writing what it means to
assume true for n=k, 4 points for showing true for n=k+1, and 1 point for correctly writing the
conclusion.

I will be taking off points for unbalanced or missing parentheses: "k + 1 ( k + 2)" is wrong if it
should be "( k + 1 ) ( k + 2 )".