For the following, determine whether the sequence is geometric. If so, find the common ratio.

$$5,5.2,5.4,5.6,5.8, \ldots$$

For the following, write the first four terms of the sequence.

$$a_n=\frac{2 n+1}{n^3}$$

For the following exercise, determine whether to use the Addition Principle or the Multiplication Principle. Then perform the calculations.

How many outcomes are possible from tossing a pair of coins?

Write an explicit formula for the geometric sequence $4,-\frac{4}{3}, \frac{4}{9},-\frac{4}{27}, \ldots$

For the following, write the first five terms of the arithmetic sequence given the first term and common difference.

$$a_1=-25, d=-9$$

For the following, express each arithmetic sum using summation notation.

$5+10+15+20+25+30+35+40+45+50$

For the following, evaluate the binomial coefficient.

$$\left(\begin{array}{l}25 \\ 11\end{array}\right)$$

What is a geometric sequence?

Write the first four terms of the sequence defined by the recursive formula $a_1=2, a_n=a_{n-1}+n$.

What is a binomial coefficient, and how it is calculated?

What term is used to express the likelihood of an event occurring? Are there restrictions on its values?

If so, what are they? If not, explain.

What is an $n$th partial sum?

Write the first four terms of the sequence defined by the recursive formula $a=-14, a_n=\frac{2+a_{n-1}}{2}$.

For the following exercise, assume that there are n ways an event A can happen, m ways an event B can happen, and that A and B are non-overlapping.

Use the Addition Principle of counting to explain how many ways event A or B can occur.