# Calc08_1 - 8.1 Sequences Craters of the Moon National Park...

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8.1: Sequences Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2008 Craters of the Moon National Park, Idaho

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A sequence is a list of numbers written in an explicit order. { } { } 1 2 3, , ... , , . .. n n a a a a a = n th term Any real-valued function with domain a subset of the positive integers is a sequence. If the domain is finite, then the sequence is a finite sequence . In calculus, we will mostly be concerned with infinite sequences .
A sequence is defined explicitly if there is a formula that allows you to find individual terms independently. ( 29 2 1 1 n n a n - = + Example: To find the 100 th term, plug 100 in for n : ( 29 100 100 2 1 100 1 a - = + 1 10001 =

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A sequence is defined recursively if there is a formula that relates a n to previous terms. We find each term by looking at the term or terms before it: 1 2 for all 2 n n b b n - = + Example: 1 4 b = 1 4 b = 2 1 2 6 b b = + = 3 2 2 8 b b = + = 4 3 2 10 b b = + = You have to keep going this way until you get the term you need.
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Calc08_1 - 8.1 Sequences Craters of the Moon National Park...

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