Exam 9: Sequences and Series; Counting and Probability

Solve the problem. -How many different license plates can be made using 3 letters followed by 4 digits selected from the digits 0 through 9, if neither letters nor digits may be repeated?

Provide an appropriate response. -Determine the general term of the sequence $11 , \frac { 11 } { 2 } , \frac { 11 } { 4 } , \frac { 11 } { 8 } , \frac { 11 } { 16 } , \ldots$

Solve the problem. -How many 5-card poker hands consisting of three 10's and two cards that are not 10's are possible in a 52-card deck?

Solve the problem. -Lisa has 5 skirts, 6 blouses, and 4 jackets. How many 3-piece outfits can she put together assuming any piece goes with any other?

Find the indicated term of the arithmetic sequence. - $\frac { 5 } { 9 } , \frac { 2 } { 3 } , \frac { 7 } { 9 } , \ldots ; a _ { 16 }$

The first several terms of a sequence are given. Find the indicated partial sum. - $- 7 , - 5 , - 3 , - 1 , \ldots ; S _ { 5 }$

Solve the problem. -How many different license plates can be made using 2 letters followed by 4 digits selected from the digits 0 through 9, if letters and digits may be repeated?

Find the general term of the arithmetic sequence then find the indicated term of the sequence. Assume that the domain of the sequence is all natural numbers. -Find an and a35.

Find the indicated term of the arithmetic sequence. -Given an arithmetic sequence with d $\mathrm { d } = - 6 \text { and } \mathrm { a } _ { 4 } = 10$ find a20.

Find the indicated sum. -3 + 6 + 9 + . . . + 120

Find the probability. -What is the probability that a card drawn from a deck of 52 cards is not a spade?

Provide an appropriate response. -Find the 8th term of the geometric sequence whose first term is 6 and whose common ratio is -3.

Write a formula for the general term, or nth term, for the given sequence. - $\frac { 1 } { 9 } , \frac { 8 } { 9 } , \frac { 64 } { 9 } , \frac { 512 } { 9 } , \ldots$

Solve the problem. -After being struck with a hammer, a gong vibrates 21 vibrations in the first second and in each second thereafter makes $\frac { 3 } { 4 }$ as many vibrations as in the previous second. Find how many vibrations the gong makes before it stops vibrating.

Solve the problem. -A committee is to be formed consisting of 5 men and 3 women. If the committee members are to be chosen from 13 men and 14 women, how many different committees are possible?

Solve the problem. -Suppose you are offered a job with a starting salary of $37,000 per year and a guaranteed raise of $1500 per year. How much money will you make in total over the first 20 years?

Write the first four terms of the recursive sequence. - $a _ { 1 } = 8 , a _ { n } = 1 - \frac { 1 } { a _ { n - 1 } }$ for $n \geq 2$

Use the Binomial Theorem to expand the binomial. - $( 2 x - 1 ) ^ { 5 }$

Solve the problem. -A restaurant offers a choice of 5 salads, 9 main courses, and 4 desserts. How many possible 3-course meals are there?

Solve the problem. -A basketball player with a free throw shooting percentage of 80% gets fouled and goes to the line to shoot two free throws. What are the odds of her making her first shot?