Write recursive formulas for sequences, including the Fibonacci sequence.
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Consider the sequence below.
$${1, \space1,\space 2,\space 3,\space 5,\space 8,\space 13,\space 21, \space34, …}$$
a. Describe the pattern that you notice. How is each next term determined?
b. This pattern is famously called the Fibonacci sequence. Write a recursive formula to represent the Fibonacci sequence. Write a formula in sequence notation using $${a_n}$$ and in formula notation using $${f(n)}$$.
c. If $${a_{15}=610}$$ and $${a_{16}=987}$$, what are the values of $${a_{17}}$$ and $${a_{14}}$$?
For each sequence below, write a recursive formula, in both sequence notation and function notation, to represent the sequence.
a. $${18,\space 13,\space 8,\space 3,\space -2,\space …}$$
b. $${4,\space 12,\space 36,\space 108,\space 324,\space …}$$
A sequence is given by an explicit formula, as shown below, where $$n$$ represents the term number.
$$a_n=4n-1$$ for $$n\geq1$$
a. Write the first five terms in the sequence.
b. Write a recursive formula to represent the sequence.
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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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Consider the sequence following a minus $$8$$ pattern: $${9,\space1,\space-7,\space-15\space,...}$$
Write a recursive formula for the sequence.
Algebra I > Module 3 > Topic A > Lesson 2 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..
Consider the sequence given by the formula $${a(n+1)=5a(n)}$$ and $${a(1)=2}$$ for $${n\geq1}$$
Algebra I > Module 3 > Topic A > Lesson 2 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..