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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?
September 13, 2017
Sequence
Term
Arithmetic Sequence
Common Difference
September 13, 2017
Find the next four terms of the arithmetic sequence 91, 83, 75, . . .
We use some specific notation -
September 13, 2017
So the formulas, or rules, for the nth term of an arithmetic sequence are
September 13, 2017
September 13, 2017
An explicit formula
A recursive formula
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
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
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, . . .?
September 13, 2017
September 13, 2017
Write rules for these sequences:
1. a2 = 7 and a5 = 13
2. a5 = 17 and a15 = 77
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?
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.
September 13, 2017
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