Transcription of 8.3 ARITHMETIC AND GEOMETRIC SEQUENCES
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8.3 ARITHMETIC AND GEOMETRIC SEQUENCES
Pg451 [R] G1 5-36058 / HCG / Cannon & Elich cr 11-30-95 MP1. Airthmetic and GEOMETRIC SEQUENCES 451. ARITHMETIC AND GEOMETRIC SEQUENCES . Whenever you tell me that mathematics is just a human invention like the game of chess I would like to believe you. But I keep returning to the same problem. Why does the mathematics we have discovered in the past so often turn out to describe the workings of the Universe? John Barrow I remember that when I Two kinds of regular SEQUENCES occur so often that they have specific names, was about twelve I learned ARITHMETIC and GEOMETRIC SEQUENCES . We treat them together because some obvi- from [my uncle] that by the ous parallels between these kinds of SEQUENCES lead to similar formulas. This also distributive law 21 times makes it easier to learn and work with the formulas.
Both arithmetic and geometric sequences begin with an arbitrary first term, and the sequences are generated by regularly adding the same number (thecom-mon difference in an arithmetic sequence) or multiplying by the same number (the common ratio in a geometric sequence). Definitions emphasize the parallel fea-tures, which examples will clarify.
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