2-1 Arithmetic Sequences

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1Definitions & Equations

Writing & Solving Arithmetic Sequences

Practice Problems

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Definitions

Sequence A list of numbers in a particular order

Term Each number in the sequence

Arithmetic Sequence A sequence in which each term can be

found by adding a constant Common Difference (d)

The constant by which the arithmetic sequence changes

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nth Term of an Arithmetic Sequence

an is the final term of the sequence a1 is the first term in the sequence d is the common difference n is the number of terms

Can be any positive integer

1 ( 1)na a d n

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Finding a Particular Term

Using the table provided, find how much it would cost to rent a crane for 12 monthsMonths Cost ($)

1 75,000

2 90,000

3 105,000

4 120,000

1 ( 1)na a d n

12 75,000 15,000(12 1)a

12 240,000a

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Write an Equation for the nth Term

Write an equation for the nth term of the sequence 8, 17, 26, 35…

1 ( 1)na a d n

8 9( 1)na n

8 9 9na n

9 1na n

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Arithmetic Means

The terms between any two nonsuccessive terms of an arithmetic sequence

19,30,41,52,63,74,85,96,...19, , 41,52,63, ,85,9630 74 ,..., 41,5230 ,63,743 arithmetic means

, 430 1,52,63 ,74

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Finding Arithmetic Means

Find the four arithmetic means between 16 and 91.16,?,?,?,?,91...

1 ( 1)na a d n

91 16 (6 1)d 91 16 5d 75 5d

15d

+15 +15 +15 +15

16 31 46 61 76

31,46,61,76

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Practice Problems

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More Practice Problems