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Sullivan Algebra and Trigonometry: Section 13.2 Objectives of this Section Determine If a Sequence Is Arithmetic Find a Formula for an Arithmetic Sequence Find the Sum of an Arithmetic Sequence

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An arithmetic sequence is defined as d is called the common difference between terms of the sequence. The terms of an arithmetic sequence with the first term a and common difference d follow the pattern: a, a + d, a + 2d, a + 3d, …..

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Common difference does not depend on n, therefore the sequence is arithmetic.

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The nth Term of an Arithmetic Sequence

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The 6th term of an arithmetic sequence is 31. The 19th term is 109. Find the first term and the common difference. Give a recursive formula for the sequence.

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So, the nth term is: To find the n+1 term in terms of the nth term:

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Sum of n Terms of an Arithmetic Sequence

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Find the sum of the first 30 terms of the sequence {7n + 2}. That is, find 9 + 16 + 23 +... + 212

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