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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. The greatest value in this 21 equals 11. I thought that was great. association is understanding how the ideas are related and how to derive the Peter Lax formulas from fundamental concepts.

sequences. For an arithmetic sequence we get thenth term by adding d to the first term n 2 1 times; for a geometric sequence, we multiply the first term byr, n 2 1 times. Formulas for the nth terms of arithmetic and geometric sequences For an arithmetic sequence, a formula for thenth term of the sequence is a n 5 a 1 ~n 2 1!d. (1)

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