91Ó°ÊÓ

Finding a Term of a Geometric Sequence Find the indicated term of the geometric sequence. $$a_{1}=5, a_{3}=\frac{45}{4}, 8 \mathrm{th} \text { term }$$

One card is selected at random from a standard deck of 52 playing cards. Use a formula to find the probability of the union of the two events. The card is a heart or a spade.

Use the table, which shows the age groups of students in a college sociology class. $$\begin{array}{|c|c|} \hline \text { Age } & \text { Number of students } \\ \hline 18-19 & 11 \\ \hline 20-21 & 18 \\ \hline 22-30 & 2 \\ \hline 31-40 & 1 \\ \hline \end{array}$$ A student from the class is randomly chosen for a project. Find the probability that the student is the given age. 18 or 19 years old

Use the Binomial Theorem to expand and simplify the expression. \(\left(\frac{1}{x}+y\right)^{5}\)

Use the letters \(\mathbf{A}, \mathbf{B}, \mathbf{C},\) and \(\mathbf{D}\). Write all permutations of the letters.

Finding a Term of a Geometric Sequence Find the indicated term of the geometric sequence. $$a_{2}=-18, a_{5}=\frac{2}{3}, 6 \text { th term }$$

Write an expression for the apparent \(n\) th term of the sequence. (Assume \(n\) begins with \(1 .\)) $$\frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}, \frac{6}{7}, \dots$$

The first two terms of the arithmetic sequence are given. Find the missing term. Use the table feature of a graphing utility to verify your results. $$a_{1}=4.2, \quad a_{2}=1.8, \quad a_{7}=\square$$

The first two terms of the arithmetic sequence are given. Find the missing term. Use the table feature of a graphing utility to verify your results. $$a_{1}=-0.7, a_{2}=-13.8, a_{8}=\square$$

Write an expression for the apparent \(n\) th term of the sequence. (Assume \(n\) begins with \(1 .\)) $$\frac{2}{1}, \frac{3}{3}, \frac{4}{5}, \frac{5}{7}, \frac{6}{9}, \dots$$