CBC-Chp-11-2-NTs - CalcBC Chp 11-2 Series (Geometric) NOTES...

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CalcBC Chp 11-2 Series (Geometric) NOTES 1. SEQUENCES SEQUENCE – ordered list of numbers, a 1 , a 2 , a 3 , a 4 , , a n Sequences are organized by three categories: arithmetic, geometric, and neither ARITHMETIC SEQUENCE – sequence formed by adding the same amount to each term Ex(arithmetic)-- 2, 5, 8, 11, 14, 17, Ex(not arithmetic)-- 2, 5, 8, 12, 15, 18, What is the COMMON DIFFERENCE? No common difference. 3 is the common difference because it No common difference because 3 is added for some is the amount added to each term to get terms and 4 is added for one of them the next term. GEOMETRIC SEQUENCE -- sequence formed by multiplying the same amount to each term Ex(geometric)-- 2, −6, 18, −54, 162, − 486, Ex(not geometric)-- 2, 6, 18, 54, 108, 324, What is the COMMON RATIO? No common ratio. 3 is the common ratio because it No common ratio because 3 is multiplied for some is the amount multiplied to each term terms and 2 is multipled for one of them to get the next term. Ex(geometric)-- a, ar, ar 2 , ar 3 , ar 4 , Ex(geometric)-- 8, 4, 2, 1, ½ , ¼ , , What is the common ratio? _______ What is the common ratio? _______ What are the next two terms? ______________ What are the next two terms? ______________ GEOMETRIC SEQUENCES have a predictable general term. EXPLICIT FORMULA for the GEOMETRIC GENERAL TERM:
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This note was uploaded on 02/21/2011 for the course MATH 408C taught by Professor Knopf during the Spring '10 term at University of Texas at Austin.

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CBC-Chp-11-2-NTs - CalcBC Chp 11-2 Series (Geometric) NOTES...

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