Define arithmetic and geometric sequences, and identify common ratios and common differences in sequences.
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Four sequences are shown below. Which one does not belong and why?
$${4, 8, 12, 16, 20 ...}$$ | $${50, 46, 42, 38, 34, ...}$$ |
$${1, 4, 16, 64, 216, ...}$$ | $${1600, 400, 100, 25, 12.5, ...}$$ |
Complete each sequence by filling in the missing terms. Then identify each sequence as arithmetic or geometric and name the common difference or common ratio.
a. $${-2}$$, $$4$$, ___, ___, ___, $${28}$$, ...
b. $${{1\over2}}$$, ___, ___, $$4$$, $$8$$, ___, …
c. $$5$$, ___, ___, ___, $${2{1\over3}}$$, $${1{2\over3}}$$, ...
d. ___, $$3$$, $${-9}$$, ___, $$-81$$, ___, …
Write a recursive formula for each sequence.
a. $${11, \space14,\space 17,\space 20,\space 23, …}$$
b. $${{1\over9},\space {1\over3},\space1,\space 3,\space 9,\space …}$$
c. $${32,\space 16,\space 8,\space 4,\space 2,\space …}$$
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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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Write the first three terms in the following sequences. Identify them as arithmetic or geometric.
Algebra I > Module 3 > Topic A > Lesson 3 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Identify each sequence as arithmetic or geometric. Explain your answer and write a recursive formula for the sequence.
a. $${14,11,8,5,…}$$
b. $${2,10,50,250,…}$$
c. $${-{1\over2}, -{3\over2}, -{5\over2},-{7\over2},...}$$
Algebra I > Module 3 > Topic A > Lesson 3 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Modified by Fishtank Learning, Inc.