Chapter 9

Write an expression for the apparent \(n\) th term of the sequence. (Assume \(n\) begins with \(1 .\)) $$\frac{1}{3},-\frac{2}{9}, \frac{4}{27},-\frac{8}{81}, \dots$$

Use a graphing utility to graph the first 10 terms of the sequence. (Assume \(n\) begins with 1.) $$a_{n}=-5+2 n$$

Find the number of distinguishable permutations of the group of letters. \(\mathbf{B}, \mathbf{B}, \mathbf{B}, \mathbf{T}, \mathbf{T}, \mathbf{T}, \mathbf{T}, \mathbf{T}\)

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 to 21 years old

Graphing the Terms of a Sequence Use a graphing utility to graph the first 10 terms of the sequence. $$a_{n}=20(0.85)^{n-1}$$

Use the Binomial Theorem to expand and simplify the expression. \(\left(\frac{2}{x}-3 y\right)^{5}\)

$$1+\frac{1}{1}, 1+\frac{1}{2}, 1+\frac{1}{3}, 1+\frac{1}{4}, 1+\frac{1}{5}, \dots$$$$1+\frac{1}{1}, 1+\frac{1}{2}, 1+\frac{1}{3}, 1+\frac{1}{4}, 1+\frac{1}{5}, \dots$$

Use a graphing utility to graph the first 10 terms of the sequence. (Assume \(n\) begins with 1.) $$a_{n}=0.4 n-2$$

Find the number of distinguishable permutations of the group of letters. \(\mathbf{A}, \mathbf{L}, \mathbf{G}, \mathbf{E}, \mathbf{B}, \mathbf{R}, \mathbf{A}\)

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. Older than 21 years old

Graphing the Terms of a Sequence Use a graphing utility to graph the first 10 terms of the sequence. $$a_{n}=2(1.3)^{n-1}$$

Use the Binomial Theorem to expand and simplify the expression. \((4 x-1)^{3}-2(4 x-1)^{4}\)

Write an expression for the apparent \(n\) th term of the sequence. (Assume \(n\) begins with \(1 .\)) $$1+\frac{1}{3}, 1+\frac{1}{6}, 1+\frac{1}{11}, 1+\frac{1}{18}, 1+\frac{1}{27}, \ldots$$

Use a graphing utility to graph the first 10 terms of the sequence. (Assume \(n\) begins with 1.) $$a_{n}=-1.3 n+7$$

Find the number of distinguishable permutations of the group of letters. \(\mathbf{M}, \mathbf{I}, \mathbf{S}, \mathbf{S}, \mathbf{I}, \mathbf{S}, \mathbf{S}, \mathbf{I}, \mathbf{P}, \mathbf{P}, \mathbf{I}\)

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. Younger than 31 years old

Graphing the Terms of a Sequence Use a graphing utility to graph the first 10 terms of the sequence. $$a_{n}=10(-1.2)^{n-1}$$

Use the Binomial Theorem to expand and simplify the expression. \((x+3)^{5}-4(x+3)^{4}\)

Write an expression for the apparent \(n\) th term of the sequence. (Assume \(n\) begins with \(1 .\)) $$1,3,1,3,1, . . .$$

Use the table feature of a graphing utility to find the first 10 terms of the sequence. (Assume \(n\) begins with 1.) $$a_{n}=4 n-5$$

Evaluate \(_{n} C_{r}\) using the formula from this section. $$_{5} C_{2}$$

A random number generator selects three numbers from 1 through 10. Find the probability of the event. All three numbers are even.

Finding a Sequence of Partial Sums In Exercises 51 and \(52,\) find the sequence of the first five partial sums \(S_{1}, S_{2}\) \(S_{3}, S_{4},\) and \(S_{5}\) of the geometric sequence by adding terms. $$8,-4,2,-1, \frac{1}{2}, \ldots$$

Use the Binomial Theorem to expand and simplify the expression. \(3(x+1)^{5}+4(x+1)^{3}\)

Write an expression for the apparent \(n\) th term of the sequence. (Assume \(n\) begins with \(1 .\)) $$1,-1,1,-1,1, \ldots$$

Use the table feature of a graphing utility to find the first 10 terms of the sequence. (Assume \(n\) begins with 1.) $$a_{n}=17+3 n$$

Evaluate \(_{n} C_{r}\) using the formula from this section. $$_{6} C_{3}$$

Finding a Sequence of Partial Sums In Exercises 51 and \(52,\) find the sequence of the first five partial sums \(S_{1}, S_{2}\) \(S_{3}, S_{4},\) and \(S_{5}\) of the geometric sequence by adding terms. $$8,12,18,27, \frac{81}{2}, \ldots$$

Use the Binomial Theorem to expand and simplify the expression. \(2(x-3)^{4}+5(x-3)^{2}\)

Write the first five terms of the sequence defined recursively. $$a_{1}=28, a_{k}=a_{k-1}-4$$

Use the table feature of a graphing utility to find the first 10 terms of the sequence. (Assume \(n\) begins with 1.) $$a_{n}=20-\frac{3}{4} n$$

Evaluate \(_{n} C_{r}\) using the formula from this section. $$_{4} C_{1}$$

A random number generator selects three numbers from 1 through 10. Find the probability of the event. All three numbers are less than or equal to 3.

Finding a Sequence of Partial Sums Use a graphing utility to create a table showing the sequence of the first 10 partial sums \(S_{1}, S_{2}, S_{3}, \ldots\) and \(S_{10}\) for the series. $$\sum_{n=1}^{\infty} 16\left(\frac{1}{2}\right)^{n-1}$$

Use the Binomial Theorem to expand and simplify the expression. \(-3(x-2)^{3}-4(x+1)^{6}\)

Write the first five terms of the sequence defined recursively. $$a_{1}=15, a_{k}=a_{k-1}+3$$

Use the table feature of a graphing utility to find the first 10 terms of the sequence. (Assume \(n\) begins with 1.) $$a_{n}=\frac{4}{5} n-3$$

Evaluate \(_{n} C_{r}\) using the formula from this section. $$_{7} C_{1}$$

A random number generator selects three numbers from 1 through 10. Find the probability of the event. All three numbers are greater than or equal to \(9 .\)

Finding a Sequence of Partial Sums Use a graphing utility to create a table showing the sequence of the first 10 partial sums \(S_{1}, S_{2}, S_{3}, \ldots\) and \(S_{10}\) for the series. $$\sum_{n=1}^{\infty} 4(0.2)^{n-1}$$

Use the Binomial Theorem to expand and simplify the expression. \(-5(x+2)^{5}-2(x-1)^{2}\)

Write the first five terms of the sequence defined recursively. $$a_{1}=3, a_{k+1}=2\left(a_{k}-1\right)$$

Use the table feature of a graphing utility to find the first 10 terms of the sequence. (Assume \(n\) begins with 1.) $$a_{n}=1.5+0.05 n$$

Evaluate \(_{n} C_{r}\) using the formula from this section. $$_{25} C_{0}$$

A random number generator selects three numbers from 1 through 10. Find the probability of the event. Two numbers are less than 5 and the other number is \(10 .\)

Finding the Sum of a Finite Geometric Sequence Find the sum. Use a graphing utility to verify your result. $$\sum_{n=1}^{9} 2^{n-1}$$

Find the specified \(n\) th term in the expansion of the binomial. \((x+8)^{10}, n=4\)

Write the first five terms of the sequence defined recursively. $$a_{1}=32, a_{k+1}=\frac{1}{2} a_{k}$$

Use the table feature of a graphing utility to find the first 10 terms of the sequence. (Assume \(n\) begins with 1.) $$a_{n}=8-12.5 n$$

Evaluate \(_{n} C_{r}\) using the formula from this section. $$_{20} C_{0}$$