Unit 1 Topics

Arithmetic Sequences (formula) Arithmetic Series (formula) Sigma Notation Recursive Sequences Geometric Sequences (formula) Geometric Series (formula)

CC Algebra 2 - R Name: ______________________________Arithmetic Sequences

CC Algebra 2 - R Name: ______________________________Arithmetic Sequences - Regents

1. What is the common difference of the arithmetic sequence ?

1)

2)3) 34) 9

2. Which arithmetic sequence has a common difference of 4?1)2)3)4)

3. What is a formula for the nth term of sequence B shown below?

1)2)3)4)

CC Algebra 2 - Regents Name: ______________________________Arithmetic Sequences and Series Applications

Problem 1

Problem 2

Problem 3

The distance an object falls per second while only under the influence of gravity forms an arithmetic sequence with it falling 16 feet in the first second, 48 feet in the second, 80 feet in the third, etc. What is the total distance an object will fall in 10 seconds? Show the work that leads to your answer.

CC Algebra 2 - Regents Name: _______________________Sigma Notation

1. What is the value of 1) 582) 543) 534) 50

2. Evaluate:

3. What is the value of ?1) 12) 23) 34) 0

4. The expression is equal to1)2)3)4)

5. Evaluate: 6. Evaluate:

7. Which summation represents ?

1)

8. Mrs. Hill asked her students to express the sum using sigma notation. Four different student answers were given. Which student answer is correct?

2)

3)

4)

1)

2)

3)

4)

9. Which expression represents the sum of the sequence ?

1)

2)

3)

4)

10. Jonathan’s teacher required him to

express the sum using sigma notation. Jonathan proposed four possible answers. Which of these four answers is not correct?1)

2)

3)

4)

11. Express the sum using sigma notation.

Recursive Sequences

Find the first five terms of each sequence.

Ex. a1=5, an=an-1+1 Ex. a1=1, an+1=3an Ex. a1=1, an=2an-

1+1

Find the first six terms of each sequence.

1. a1=-2, an=-2an-1 2. a1=20, an=an-1 – 4 3. a1=4, an+1=an+n

Old Regents Questions

1. Find the first four terms of the recursive sequence defined below.

2. Find the third term in the recursive sequence , where .

CC Algebra 2 – Regents Name: _____________________________Sequences and Series

1. The formula below can be used to model which scenario?

2. The population of Jamesburg for the years 2010-2013,

1) The first row of a stadium has 3000 seats, and each row thereafter has 80 more seats than the row in front of it.

2) The last row of a stadium has 3000 seats, and each row before it has 80 fewer seats than the row behind it.

3) A bank account starts with a deposit of $3000, and each year it grows by 80%.

4) The initial value of a specialty toy is $3000, and its value each of the following years is 20% less.

respectively, was reported as follows:

250,000 250,937 251,878 252,822

How can this sequence be recursively modeled?1)2)3)

4)

Algebra 2 CC Name: _______________________Geometric Sequences

Algebra 2 CC Name: _______________________Geometric Sequences

1. What is the common ratio of the geometric sequence shown below?

1)

2) 23)4)

2. What is the common ratio of the geometric sequence whose first term is 27 and fourth term is 64?1)

2)

3)

4)

3. What is the common ratio of the sequence

?1)

2)

3)

4)

4. A sequence has the following terms: ,

, , . Which formula represents the nth term in the sequence?1)2)3)

4)

Algebra 2 – CC Name: ________________________

QUIZ #1

1. Evaluate: 2. Evaluate:

Find the 43rd term of each sequence.

3. 21, 15, 9, 3, . . . 4. 54, 18, 6, . . .

5. Find the first five terms in the recursive sequence , where .

6. Elaina has decided to run the Buffalo half-marathon in May. She researched training plans on the Internet and is looking at two possible plans: Jillian’s 12-week plan and Josh’s 14-week plan. The number of miles run per week for each plan is plotted below.

a. Which one of the plans follows an arithmetic pattern? Explain how you arrived at your answer.

b. Write a recursive definition to represent the number of miles run each week for the duration of the plan you chose.

c. Jillian’s plan has an alternative if Elaina wanted to train instead for a full 26-mile marathon. Week one would start at 13 miles and follow the same pattern for the half-marathon, but it would continue for 14 weeks. Write an explicit formula, in simplest form, to represent the number of miles run each week for the full-marathon training plan.

Evaluate the series for the specified number of terms.

6. 54 + (-36) + 24 + (-16) . . . ; n =27 7. –2 + 2 + 6 + 10 + . . . ; n =100

8. Write the following series using sigma notation: 9+17+25+33+41+49

9. In an arithmetic sequence, and . Determine a formula for , the term of this sequence.

10. Write an explicit formula for , the nth term of the recursively defined sequence below.

Algebra 2 Name: ________________________Probability

Probability

Examples:

1. A student is to roll a die and flip a coin. How many possible outcomes will there be?

2. For a college interview, Robert has to choose what to wear from the following: 4 slacks, 3 shirts, 2 shoes and 5 ties. How many possible outfits does he have to choose from?

3. Determine the number of outcomes for:

a) Tossing a regular die three times.b) Tossing a coin five times.c) Ordering two different flavors of ice cream at Baskin Robbins.

Examples:

1. How many ways can the letters ABC be arranged?

Counting Principle -

Permutation -

2. A combination lock will open when the right choice of three different numbers (from 1 to 30, inclusive) is selected. How many different lock combinations is possible assuming no number is repeated?

3. From a club of 24 members, a President, Vice President, Secretary, Treasurer and Historian are to be elected. In how many ways can the offices be filled?

Examples:

1. To play a particular card game, each player is dealt five cards from a standard deck of 52 cards. How many different hands are possible?

2. A student must answer 3 out of 5 essay questions on a test. In how many different ways can the student select the questions?

3. A basketball team consists of two centers, five forwards, and four guards. In how many ways can the coach select a starting lineup of one center, two forwards, and two guards?

Combination –

Algebra 2 Name: ________________________Ms. P. St.Agathe

Permutations/Combinations

1. A four-digit serial number is to be created from the digits 0 through 9. How many of these serial numbers can be created if 0 can not be the first digit, no digit may be repeated, and the last digit must be 5?

1) 4482) 5043) 2,2404) 2,520

2. Find the total number of different twelve-letter arrangements that can be formed using the letters in the word PENNSYLVANIA.

3. The letters of any word can be rearranged. Carol believes that the number of different 9-letter arrangements of the word “TENNESSEE” is greater than the number of different 7-letter arrangements of the word “VERMONT.” Is she correct? Justify your answer.

4. How many different three-member teams can be selected from a group of seven students?

1) 12) 353) 2104) 5,040

5. The principal would like to assemble a committee of 8 students from the 15-member student council. How many different committees can be chosen?

1) 1202) 6,4353) 32,432,4004) 259,459,200

Algebra CC - Regents Name: ________________________

Basic Probability

Exercise #2: Given the basic definition of probability, between what two numbers must ALL probabilities lie? Explain.

Algebra 2 Regents - CC Name: ________________________

Probability: Sets