11-14 Class notes

Preparation for surprise quiz or open note quiz:
Fill in formulas on page 94, item 16

common ratio of a geometric sequence or series = ____________
the next term divided by the current term

nth term "a sub n" of a geometric series = ____________
the first term times the common ratio r raised to the power n minus 1

partial sum "S sub n" of a geometric series = ____________
the first term times ( 1 minus the common ratio to the nth power / 1 minus the common ratio )

infinite sum "S" of a geometric series = ____________
the first term divided by ( 1 minus the common ratio )


Homework for 10-15 and 10-16:  Embedded Assessment 1 The Chessboard Problem

Since the knight takes home all the money on all the squares, we need to think about a series from which we can calculate a partial sum S sub n.

n = 5 or n = 20 or n = 64

In the arithmetic series option, a sub 1 = $1000 = 100000 cents and difference "d" = $1000
Use the formulas for arithmetic series on page 84

common difference of an arithmetic sequence or series = ____________
the next term minus the current term

nth term "a sub n" of an arithmetic series = ____________
the first term plus the common difference d times (n-1)

partial sum "S sub n" of a geometric series = ____________
(the first term a sub 1 plus the last term a sub n) times (n/2)



In the geometric series option, a sub 1 =  1 cent and the ratio "r" = 2
Use the formulas for geometric series on page 94