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2

Sequences and Series

Arithmetic Sequences and

Series

Geometric Sequences and

Series

Counting Principles

Probability

100 100 100 100 100

200 200 200 200 200

300 300 300 300 300

400 400 400 400 400

500 500 500 500 500

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Sequences and Series100

• Determine if the following sequences are arithmetic, geometric, or neither.

1. -9, -5, -1, 3, …

2. 0, 5, 15, 30, 50, …

3. -½, 1, -2, 4, …

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Sequences and Series200

• Write the first four terms of the sequence

an =n+ 22n

5

Sequences and Series300

• Write the first three terms of the sequencewhere a1 = -2.

an =3an−1 + 2

6

Sequences and Series400

• Find the sum

(2k −3)

k=5

10

∑

7

Sequences and Series500

• Write the following sum in sigma notation. [(1)2 – 5] + [(2)2 – 5] + [(3)2 – 5] + … + [(10)2 – 5]

8

Arithmetic Sequences and Series100

• Find the 20th term of the arithmetic sequence. 10, 5, 0, -5, -10, ….

9

Arithmetic Sequences and Series200

• Find the 19th term of the arithmetic sequence a1 = 5, a4 = 15

10

Arithmetic Sequences and Series300

• Find the 1st term of the arithmetic sequence with a5 = 190 and a10 = 115.

11

Arithmetic Sequences and Series400

• Find the 1001st term of the sequence with a1 = -4 and a5 = 16.

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Arithmetic Sequences and Series500

• Use the Gauss formula to find the sum of the first 30 terms of the sequence -30, -23, -16, -9, …

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Geometric Sequences and Series100

• Find the 6th term of the geometric sequence with a1 = 64 and r = -1/4.

14

Geometric Sequences and Series200

• Find the 22nd term of the sequence 4, 8, 16, …

15

Geometric Sequences and Series300

Sum of first n terms = S

n=a1

1−rn

1−r⎛

⎝⎜⎞

⎠⎟

Sum of infinite # of terms = S =

a1

1−r

• Find the sum of the infinite geometric sequence 6, 2, 2/3, ….

16

Geometric Sequences and Series400

Sum of first n terms = S

n=a1

1−rn

1−r⎛

⎝⎜⎞

⎠⎟

Sum of infinite # of terms = S =

a1

1−r

• Find S10 for the sequence 7, 14, 28, …

17

Geometric Sequences and Series500

• Find S16 for the sequence 200, 50, 12.5, …

Sum of first n terms = S

n=a1

1−rn

1−r⎛

⎝⎜⎞

⎠⎟

Sum of infinite # of terms = S =

a1

1−r

18

Counting Principles100

• In how many ways can a 7 question True-False exam be answered?

• Do you use permutations, combinations, or a slot-method to solve the problem?

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Counting Principles200

• How many distinct license plates can be issued consisting of one letter followed by a three-digit number? (Suppose the numbers CAN repeat)

• Do you use permutations, combinations, or a slot-method to solve the problem?

20

Counting Principles300

• The Statistics class needs 10 students to answer a survey. Mrs. Cox has 15 students in her 4th period Algebra 2 class. In how many different ways can she choose the 10 students?

• Do you use permutations, combinations, or a slot-method to solve the problem?

21

Counting Principles400

• Compute the following without a calculator.1. 6!

2. 7P2

3. 5C2

22

Counting Principles500

• An exacta in horse racing is when you correctly guess which horses will finish first and second.   If there are eight horses in the race, how many different possible outcomes for the exacta are there?

• Do you use permutations, combinations, or a slot-method to solve the problem?

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Probability100

• What are the odds of getting a “tails” when flipping a fair coin? What is the probability?

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Probability200

• What is the probability you roll a 7 or 11 with a pair of dice?

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Probability300

• What is the probability of getting a 100% on a 5 question multiple-choice test with options A, B, C, and D?

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Probability400

• There is a raffle at the end of the year in Mrs. Cox’s class. When a name is drawn, it is placed back into the box. There are three prizes – an iPod worth $150, $100 in cash, and an iPad worth $800. To help offset the price of these items, she charges $10 for a ticket (the rest of the money was donated). Each of Mrs. Cox’s students gets one ticket. She has 65 students. What is the expected value? Should you participate in the raffle?

27

Probability500

27

• A bag contains 3 red, 4 green, 2 blue, and 1 purple candy. A piece of candy is selected, it is eaten, and then a second piece is selected. Draw a tree diagram. What is the probability of the following events?

1. P(2 red)

2. P(2 purple)

3. P(1 green and 1 blue)