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September 13, 2017 A radio station is having a contest in which listeners can win $1000 by answering a trivia question correctly. Every time the question is answered incorrectly $100 is added to the prize. Suppose you are the 8th caller - and the first to answer correctly. How much money do you win? Arithmetic Sequences Number of calls Amount of prize money Questions: Could we graph the data from this table? What would the graph look like?

Arithmetic Sequences - Washington-Liberty...Arithmetic Sequences Number of calls Amount of prize money Questions: Could we graph the data from this table? What would the graph look

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Page 1: Arithmetic Sequences - Washington-Liberty...Arithmetic Sequences Number of calls Amount of prize money Questions: Could we graph the data from this table? What would the graph look

September 13, 2017

A radio station is having a contest in which listeners can win $1000 by answering a trivia question correctly. Every time the question is answered incorrectly $100 is added to the prize. Suppose you are the 8th caller - and the first to answer correctly. How much money do you win?

Arithmetic Sequences

Number of calls Amount of prize money

Questions:

Could we graph the data from this table?

What would the graph look like?

Page 2: Arithmetic Sequences - Washington-Liberty...Arithmetic Sequences Number of calls Amount of prize money Questions: Could we graph the data from this table? What would the graph look

September 13, 2017

Sequence

Term

Arithmetic Sequence

Common Difference

Page 3: Arithmetic Sequences - Washington-Liberty...Arithmetic Sequences Number of calls Amount of prize money Questions: Could we graph the data from this table? What would the graph look

September 13, 2017

Find the next four terms of the arithmetic sequence 91, 83, 75, . . .

We use some specific notation -

Page 4: Arithmetic Sequences - Washington-Liberty...Arithmetic Sequences Number of calls Amount of prize money Questions: Could we graph the data from this table? What would the graph look

September 13, 2017

So the formulas, or rules, for the nth term of an arithmetic sequence are

Page 5: Arithmetic Sequences - Washington-Liberty...Arithmetic Sequences Number of calls Amount of prize money Questions: Could we graph the data from this table? What would the graph look

September 13, 2017

Page 6: Arithmetic Sequences - Washington-Liberty...Arithmetic Sequences Number of calls Amount of prize money Questions: Could we graph the data from this table? What would the graph look

September 13, 2017

An explicit formula

A recursive formula

Page 7: Arithmetic Sequences - Washington-Liberty...Arithmetic Sequences Number of calls Amount of prize money Questions: Could we graph the data from this table? What would the graph look

September 13, 2017

Are these sequences arithmetic?

1. -10, -6, -2, 0, 2, 6, 10, . . .

2. 5, 11, 17, 23, 29, . . .

Find the next four terms in these sequences:

1. 12, 16, 20, . . .

2. 3, 1, -1, . . .

3. a1 = 5 and d = 3

4. a1 = 14 and d = -2

Page 8: Arithmetic Sequences - Washington-Liberty...Arithmetic Sequences Number of calls Amount of prize money Questions: Could we graph the data from this table? What would the graph look

September 13, 2017

Write rules to describe each of these sequences:

1. a1 = 5 and d = 3

2. 6, 13, 20, 27, . . .

3. a1 = 14 and d = -2

4. a1 = 9 and a15 = 37

5. a1 = -14 and a31 = -164

Page 9: Arithmetic Sequences - Washington-Liberty...Arithmetic Sequences Number of calls Amount of prize money Questions: Could we graph the data from this table? What would the graph look

September 13, 2017

Find the nth term for each of these sequences:

1. a1 = 3, d = -5, n = 24

2. a1 = -5, d = 7, n = 13

Complete: 68 is the ______th term of the sequence -2, 3, 8, . . .

What is a13 for the sequence -17, -12, -7, . . .?

Page 10: Arithmetic Sequences - Washington-Liberty...Arithmetic Sequences Number of calls Amount of prize money Questions: Could we graph the data from this table? What would the graph look

September 13, 2017

Page 11: Arithmetic Sequences - Washington-Liberty...Arithmetic Sequences Number of calls Amount of prize money Questions: Could we graph the data from this table? What would the graph look

September 13, 2017

Write rules for these sequences:

1. a2 = 7 and a5 = 13

2. a5 = 17 and a15 = 77

Page 12: Arithmetic Sequences - Washington-Liberty...Arithmetic Sequences Number of calls Amount of prize money Questions: Could we graph the data from this table? What would the graph look

September 13, 2017

Jamila bought a snowboard priced at $545. She put down $145 and made equal monthly payments. At the end of every month, she was given a statement of the balance owed. For the first four months, the balances were $361, $322, $283, and $244. If she paid the same amount each month, what was her balance at the end of 8 months?

Page 13: Arithmetic Sequences - Washington-Liberty...Arithmetic Sequences Number of calls Amount of prize money Questions: Could we graph the data from this table? What would the graph look

September 13, 2017

Arithmetic means - the terms between any two nonconsecutive terms of an arithmetic sequence

So in the sequence 14, 23, 32, 41, 50, 59, 68, 7732, 41, and 50 are the arithmetic means between 23 and 59.

If a problem asks you to find arithmetic means, it will tell you how many to look for and the values of the terms they fall between.

Find the four arithmetic means between 18 and 78.

Find the three arithmetic means between 44 and 92.

Find the three arithmetic means between 5 and -24.

Page 14: Arithmetic Sequences - Washington-Liberty...Arithmetic Sequences Number of calls Amount of prize money Questions: Could we graph the data from this table? What would the graph look

September 13, 2017