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**Ch.9 Sequences and Series**

Section 2 – Arithmetic Sequences

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**Definition: Arithmetic Sequence**

A sequence where the difference between consecutive terms is constant. This difference is the common difference. a, a + d, a + 2d, a +3d,…

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Formulas Recursive: initial condition recursive formula Explicit:

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**EXamples Is the sequence an arithmetic sequence? 1.) 3,6,9,12,15,…**

2.) 1,4,9,16,25,…

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EXamples What is the 100th term of the sequence beginning with 6, 11, …?

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EXample What are the second and third terms of the arithmetic sequences 100, __, __, 82,…

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**Definition: Arithmetic Mean**

The average of two numbers and . In an arithmetic sequence, the middle term of any three consecutive terms is the arithmetic of the other two terms.

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EXample What is the missing term of the arithmetic sequence …, 15, __, 59, …?

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EXample The numbers of seats in the first 13 rows in the section of an arena form an arithmetic sequence. Row 1 has 14 seats, row 2 has 16 seats. How many seats are in row 13?

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