Chapter 9

For the following exercises, graph the first five terms of the indicated sequence \(a_{1}=2, \quad a_{n}=\left(-a_{n-1}+1\right)^{2}\)

For the following exercises, use this scenario: a bag of M\&Ms contains 12 blue, 6 brown, 10 orange, 8 yellow, 8 red, and 4 green M\&Ms. Reaching into the bag, a person grabs 5 M\&Ms. What is the probability of getting no brown M\&Ms?

A skateboard shop stocks 10 types of board decks, 3 types of trucks, and 4 types of wheels. How many different skateboards can be constructed?

For the following exercises, use the information provided to graph the first five terms of the geometric sequence. \(a_{n}=27 \cdot 0.3^{n-1}\)

For the following exercises, write an explicit formula for each arithmetic sequence. $$ a=\left\\{\frac{1}{3},-\frac{4}{3},-3, \ldots\right\\} $$

For the following exercises, graph the first five terms of the indicated sequence \(a_{1}=1, \quad a_{n}=a_{n-1}+8\)

Use the following scenario for the exercises that follow: In the game of Keno, a player starts by selecting 20 numbers from the numbers 1 to \(80 .\) After the player makes his selections, 20 winning numbers are randomly selected from numbers 1 to \(80 .\) A win occurs if the player has correctly selected \(3,4,\) or 5 of the 20 winning numbers. (Round all answers to the nearest hundredth of a percent.) What is the percent chance that a player selects exactly 3 winning numbers?

For the following exercises, write an explicit formula for each arithmetic sequence. $$ a=\left\\{0, \frac{1}{3}, \frac{2}{3}, \ldots\right\\} $$

For the following exercises, graph the first five terms of the indicated sequence \(a_{n}=\frac{(n+1) !}{(n-1) !}\)

A car wash offers the following optional services to the basic wash: clear coat wax, triple foam polish, undercarriage wash, rust inhibitor, wheel brightener, air freshener, and interior shampoo. How many washes are possible if any number of options can be added to the basic wash?

Find the smallest value of \(n\) such that \(\sum_{k=1}^{n}(3 k-5)>100 .\)

Use explicit formulas to give two examples of geometric sequences whose \(7^{\text {th }}\) terms are \(1024 .\)

For the following exercises, write an explicit formula for each arithmetic sequence. $$ a=\left\\{-5,-\frac{10}{3},-\frac{5}{3}, \ldots\right\\} $$

Susan bought 20 plants to arrange along the border of her garden. How many distinct arrangements can she make if the plants are comprised of 6 tulips, 6 roses, and 8 daisies?

How many terms must be added before the series \(-1-3-5-7 \ldots .\) has a sum less than \(-75 ?\)

Find the \(5^{\text {th }}\) term of the geometric sequence $$ \\{b, 4 b, 16 b, \ldots\\} $$

For the following exercises, find the number of terms in the given finite arithmetic sequence. \(a=\\{3,-4,-11, \ldots,-60\\}\)

Use the following scenario for the exercises that follow: In the game of Keno, a player starts by selecting 20 numbers from the numbers 1 to \(80 .\) After the player makes his selections, 20 winning numbers are randomly selected from numbers 1 to \(80 .\) A win occurs if the player has correctly selected \(3,4,\) or 5 of the 20 winning numbers. (Round all answers to the nearest hundredth of a percent.) What is the percent chance the player selects exactly 4 winning numbers?

How many unique ways can a string of Christmas lights be arranged from 9 red, 10 green, 6 white, and 12 gold color bulbs?

Write \(0 . \overline{65}\) as an infinite geometric series using summation notation. Then use the formula for finding the sum of an infinite geometric series to convert \(0 . \overline{65}\) to a fraction.

Find the \(7^{\text {th }}\) term of the geometric sequence \(\\{64 a(-b), 32 a(-3 b), 16 a(-9 b), \ldots\\}\)

For the following exercises, find the number of terms in the given finite arithmetic sequence. \(a=\\{1.2,1.4,1.6, \ldots, 3.8\\}\)

Use the following scenario for the exercises that follow: In the game of Keno, a player starts by selecting 20 numbers from the numbers 1 to \(80 .\) After the player makes his selections, 20 winning numbers are randomly selected from numbers 1 to \(80 .\) A win occurs if the player has correctly selected \(3,4,\) or 5 of the 20 winning numbers. (Round all answers to the nearest hundredth of a percent.) How much less is a player's chance of selecting 3 winning numbers than the chance of selecting either 4 or 5 winning numbers?

The sum of an infinite geometric series is five times the value of the first term. What is the common ratio of the series?

At which term does the sequence $$ \\{10,12,14.4,17.28, \quad \ldots\\} $$ exceed \(100 ?\)

For the following exercises, find the number of terms in the given finite arithmetic sequence. \(a=\left\\{\frac{1}{2}, 2, \frac{7}{2}, \ldots, 8\right\\}\)

Use this data for the exercises that follow: In \(2013,\) there were roughly 317 million citizens in the United States, and about 40 million were elderly (aged 65 and over). \(^{2}\) If you meet a U.S. citizen, what is the percent chance that the person is elderly? (Round to the nearest tenth of a percent.)

To get the best loan rates available, the Riches want to save enough money to place \(20 \%\) down on a \(\$ 160,000\) home. They plan to make monthly deposits of \(\$ 125\) in an investment account that offers \(8.5 \%\) annual interest compounded semi-annually. Will the Riches have enough for a \(20 \%\) down payment after five years of saving? How much money will they have saved?

At which term does the sequence \(\left\\{\frac{1}{2187}, \frac{1}{729}, \frac{1}{243}, \frac{1}{81} \quad \ldots\right\\}\) begin to have integer values?

Use this data for the exercises that follow: In \(2013,\) there were roughly 317 million citizens in the United States, and about 40 million were elderly (aged 65 and over). \(^{2}\) If you meet five U.S. citizens, what is the percent chance that exactly one is elderly? (Round to the nearest tenth of a percent.)

Karl has two years to save \(\$ 10,000\) to buy a used car when he graduates. To the nearest dollar, what would his monthly deposits need to be if he invests in an account offering a \(4.2 \%\) annual interest rate that compounds monthly?

For which term does the geometric sequence \(a_{\mathrm{n}}=-36\left(\frac{2}{3}\right)^{n-1}\) first have a non-integer value?

Find the first five terms of the sequence \(a_{1}=\frac{87}{111}\), \(a_{n}=\frac{4}{3} a_{n-1}+\frac{12}{37} .\) Use the \(>\) Frac feature to give fractional results.

Use this data for the exercises that follow: In \(2013,\) there were roughly 317 million citizens in the United States, and about 40 million were elderly (aged 65 and over). \(^{2}\) If you meet five U.S. citizens, what is the percent chance that three are elderly? (Round to the nearest tenth of a percent.)

Keisha devised a week-long study plan to prepare for finals. On the first day, she plans to study for 1 hour, and each successive day she will increase her study time by 30 minutes. How many hours will Keisha have studied after one week?

For the following exercises, use the information provided to graph the first 5 terms of the arithmetic sequence. \(a_{1}=0, d=4\)

Find the \(15^{\text {th }}\) term of the sequence \(a_{1}=625\), \(a_{n}=0.8 a_{n-1}+18\).

Use this data for the exercises that follow: In \(2013,\) there were roughly 317 million citizens in the United States, and about 40 million were elderly (aged 65 and over). \(^{2}\) If you meet five U.S. citizens, what is the percent chance that four are elderly? (Round to the nearest thousandth of a percent.)

A boulder rolled down a mountain, traveling 6 feet in the first second. Each successive second, its distance increased by 8 feet. How far did the boulder travel after 10 seconds?

For the following exercises, use the information provided to graph the first 5 terms of the arithmetic sequence. \(a_{1}=9 ; a_{n}=a_{n-1}-10\)

Use this data for the exercises that follow: In \(2013,\) there were roughly 317 million citizens in the United States, and about 40 million were elderly (aged 65 and over). \(^{2}\) It is predicted that by 2030 , one in five U.S. citizens will be elderly. How much greater will the chances of meeting an elderly person be at that time? What policy changes do you foresee if these statistics hold true?

A scientist places 50 cells in a petri dish. Every hour, the population increases by \(1.5 \%\) What will the cell count be after 1 day?

Is it possible for a sequence to be both arithmetic and geometric? If so, give an example.

For the following exercises, use the information provided to graph the first 5 terms of the arithmetic sequence. \(a_{n}=-12+5 n\)

Find the first ten terms of the sequence \(a_{1}=8\), \(a_{n}=\frac{\left(a_{n-1}+1\right) !}{a_{n-1} !}\).

A pendulum travels a distance of 3 feet on its first swing. On each successive swing, it travels \(\frac{3}{4}\) the distance of the previous swing. What is the total distance traveled by the pendulum when it stops swinging?

Find the tenth term of the sequence \(a_{1}=2, a_{n}=n a_{n-1}\).

Rachael deposits \(\$ 1,500\) into a retirement fund each year. The fund earns \(8.2 \%\) annual interest, compounded monthly. If she opened her account when she was 19 years old, how much will she have by the time she is \(55 ?\) How much of that amount will be interest earned?

List the first five terms of the sequence \(a_{n}=-\frac{28}{9} n+\frac{5}{3}\)..

List the first six terms of the sequence \(a_{n}=\frac{n^{3}-3.5 n^{2}+4.1 n-1.5}{2.4 n}\).