Write explicit rules for geometric sequences and translate between explicit and recursive formulas.
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Use technology to show the graphs of geometric functions along with their explicit formulas. This is a preview of the work that students will do in upcoming lessons on exponential growth and decay.
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The formula for an explicit rule for a geometric sequence is given by $${a_n=a_1(r)^{n-1}}$$, where $$r$$ is the common ratio and $$n$$ is the term number.
Write an explicit formula for the sequence shown in each table.
Act 1: Watch the Act 1 video of the “Incredible Shrinking Dollar.” If Dan shrinks the dollar nine times like this, how big will it be? Will you still be able to see it?
a. Give a guess you know is too big.
b. Give a guess you know is too small.
c. What information would help solve this problem?
Act 2: Share the dimensions of the dollar bill provided on the website.
d. Do the changing lengths of the dollar bill follow a geometric sequence pattern or an arithmetic sequence pattern?
e. Write an explicit formula to represent the length of the dollar bill as it shrinks.
Act 3: Watch Act 3 video.
f. Calculate the actual length of the dollar bill after Dan shrank it nine times.
Incredible Shrinking Dollar by Dan Meyer is licensed under the CC BY 3.0 license. Accessed Feb. 27, 2018, 8:56 a.m..
Modified by The Match Foundation, Inc.?
The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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Given the following information, determine the explicit equation for each geometric sequence.
a. $${f(1)=8}$$, common ratio $${r=2}$$
b. $${f(1)=4,f(n)=3f(n-1)}$$
c. $${f(n)=4f(n-1);f(1)={5\over3}}$$
Which geometric sequence above has the greatest value at $${f(100)}$$?
Module 1: Sequences from Secondary Mathematics One: An Integrated Approach made available by Mathematics Vision Project under the CC BY 4.0 license. © 2016 Mathematics Vision Project. Accessed May 16, 2018, 4:29 p.m..