explain how e­mailing a joke is related to a geometric series, algebra homework help

Use the information on

page 663

to explain how e­mailing a joke is related to a geometric series. Include an explanation of how the situation could be changed to make it better to use a formula than to add terms.

11-4
Geometric Series
Main Ideas
• Find sums of
geometric series
. Find specific terms of
geometric series
New Vocabulary
geometric series
GET READY for the Lesson
Suppose you e-mail a joke to three friends on Monday. Each of those
friends sends the joke on to three of their friends on Tuesday. Each
person who receives the joke on Tuesday sends it to three more people
on Wednesday, and so on.
E-Mail Jokes
Geometric Series Notice that every day, the number of people who read
your joke is three times the number that read it the day before. By
Sunday, the number of people, including yourself, who have read the
joke is 1+3+9+ 27 +81 +243 + 729 + 2187, or 3280!
The numbers 1, 3,9,27,81, 243,729, and 2187 form a geometric sequence
in which a = 1 and r = 3. The indicated sum of the numbers in the
sequence, i + 3 + 9 + 27 +81 +243 + 729 +2187, is called a
geometric series.
To develop a formula for the sum of a geometric series, consider the series
given in the e-mail situation above. Multiply each term in the series by
the common ratio and subtract the result from the original series.
Ss = 1 + 3 + 9 + 27 +81 +243 + 729 +2187
(-) 35,- 3+9+ 27 +81 +243 + 729 + 2187 + 6561
(1 – 3)Sg = 1 + 0 + 0 + 0 + 0 + 0 + 0 + 0 – 6561
first term in series
Ss –
1- 6561
Study Tip
or 3280
last term in series multiplied by
common ratios in this case,
common ratio
Terms of
Geometric
Sequences
Remember that a, can
also be written as ar
The expression for Sg can be written as S=”1″ A rational
expression like this can be used to find the sum of any geometric series.
Lesson 11-4 Geometric Series 643