Describe and analyze sequences given their recursive formulas.
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Sequence notation is new for students and can be challenging when they are also trying to understand recursive formulas. Encourage students to describe and explain sequences out loud with their peers using language such as “previous term” and “next term.”
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A pattern of cubes is shown below.
a. Describe the pattern you see.
b. Write the pattern as a numerical sequence.
c. What is the value of term $${a_6}$$?
d. What is the value of the term $${f(8)}$$?
e. If you knew the value of the $${n^{th}}$$ term, describe how you would find the $${(n+1)^{th}}$$ term and the $${(n-1)^{th}}$$ term.
Pattern #2 is made available by Jed Butler on Visual Patterns. ©2017 visualpatterns.org. Accessed May 22, 2018, 9:55 a.m..
Below are several ways to represent the sequence shown in Anchor Problem #1. Describe how each representation models the sequence.
Which sequence is described by each recursive formula? Some formulas may describe the same sequence, and some formulas may not describe any of the sequences.
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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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Below is a recursive formula for a sequence.
$${f(1)=2}$$ ,$${{f(n)}=f(n-1)+3}$$