Exam 9: Sequences and Series; Counting and Probability

Determine if the sequence is arithmetic. If the sequence is arithmetic, find the common difference. - $a _ { 1 } = - 3 , a _ { n } = 3 a _ { n - 1 }- 4$

Solve the problem. -How many 2-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0? No digit can be used more than once.

Determine if the sequence is arithmetic. If the sequence is arithmetic, find the common difference. -an = n(n - 3)

Find the sum of the series. - $\sum _ { i = 5 } ^ { 8 } 5$

Use the Binomial Theorem to expand the binomial. - $( x + 8 ) ^ { 5 }$

Solve the problem. -From 10 names on a ballot, a committee of 4 will be elected to attend a political national convention. How many different committees are possible?

Solve the problem. -A survey revealed that 47% of people are entertained by reading books, 27% by watching TV, and 14% are entertained by both books and TV. What is the probability that a person will be entertained by books given that the person is entertained by TV? Round to the nearest thousandth.

-A 6-sided die is rolled. The sides contain the numbers 1, 2, 3, 4, 5, 6. State the number of elements in the sample space of rolling one die.

Determine if the sequence is geometric. If the sequence is geometric, find the common ratio. --3, -12, -48, -192, -768, . . .

Find the indicated term of the sequence. - $5,7,9,11 , \ldots ; \text { a }$

Solve the problem. -Ms. Patterson proposes to give her daughter Claire an allowance of $0.10 on the first day of her 12-day vacation, $0.20 on the second day, $0.40 on the third day, and so on. Find the allowance Claire would receive on the last day of her vacation.

Solve the problem. -A man has 10 shirts and 9 ties. How many different shirt and tie arrangements can he wear?

Use Pascal's triangle to expand the binomial. - $( x - 9 ) ^ { 5 }$

Provide an appropriate response. -Given a geometric sequence such that $a _ { 1 } = 8$ and $a _ { 4 } = - 512$ , find a 5.

Write the first four terms of the sequence. - $\mathrm { a } _ { \mathrm { n } } = ( - 1 ) ^ { \mathrm { n } - 1 } ( 8 \mathrm { n } - 5 )$

Solve the problem. -A new exhibit is scheduled to open at the local museum. Museum officials expect that 7000 people will visit the exhibit in its first week, and that the number of visitors will drop by 30 people per week after the first week during the first 6 months. Find the total number of visitors expected in the exhibit's first 7 weeks.

Provide an appropriate response. -Find the 5 th term of the geometric sequence $\frac { 1 } { 2 } , \frac { 1 } { 6 } , \frac { 1 } { 18 } , \ldots$

Solve the problem. -How many different 11-letter words can be formed from the letters of the word MISSISSIPPI? Leave your answer in factorial form.

The first several terms of a sequence are given. Find the indicated partial sum. - $2 , - 7,12 , - 17 , \ldots ; \mathrm { S } _ { 6 }$

Determine if the sequence is arithmetic. If the sequence is arithmetic, find the common difference. - $a _ { 1 } = 2 , a _ { n } = a _ { n - 1 } + 8$