$a_n=3(5-4n)$

$a_n=-3(2^n)$

Write the first five terms of the sequence defined by $a_1=-2$ and $a_n=3a_{n-1}+5$ for $n\ge 2.$

Evaluate ${\displaystyle \frac{(n-1)!}{n!}}.$

Find $a_7$ for the arithmetic sequence with $a_1=-3$ and $d=4.$

Find $a_8$ for the geometric sequence with $a_1=13$ and $r=-{\displaystyle \frac{1}{2}}.$

${\displaystyle \sum _{k=1}^{20}(3k-2)}$

${\displaystyle \sum _{k=1}^5\left({\displaystyle \frac{3}{4}}\right)(2^{-k})}$

${\displaystyle \sum _{k=1}^{\infty }18{\left({\displaystyle \frac{1}{100}}\right)}^k};$ write the answer as a fraction in lowest terms.

Evaluate $\left(\begin{array}{c}13\\ 0\end{array}\right)$

Expand ${(1-2x)}^4.$

Find the term containing $x^1$ in the expansion of ${(2x+1)}^4.$

In how many ways can you answer every question on a ­ true–false test containing ten questions?

P(9, 2)

C(7, 5)

A firm needs to fill two positions—one in accounting and one in human resources. How many ways can these positions be filled if there are six applicants for the accounting position and ten applicants for the human resources position?

A state is considering using license plates consisting of two letters followed by a four-digit number. How many distinct license plate numbers can be formed?

A box contains five red balls and seven black balls. What is the probability that a ball drawn at random will be red?

What is the probability that a 4 does not come up on one roll of a die?

A box contains seven quarters, six dimes, and five nickels. If two coins are drawn at random, what is the probability that both are quarters?