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

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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

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, …..

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

The nth Term of an Arithmetic Sequence

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.

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

Sum of n Terms of an Arithmetic Sequence

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

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