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.
8.3 Airthmetic and Geometric Sequences 453 (c) a n11 2 a n 5 ln~n 1 1! 2 ln n 5 ln n 1 1 n. The difference depends on n,so the sequence is not arithmetic. Checking ratios, a n11 a n 5 ln~n 1 1! ln n,sotheratio also changes with n. The sequence is neither arithmetic nor geometric. b cEXAMPLE3 Arithmetic sequences Show that the sequence is ...
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