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©Evergreen Public Schools 2011 1 8.1 Arithmetic Sequences Recursive Rules Vocabulary : arithmetic...
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©Evergreen Public Schools 2011 1 8.1 Arithmetic Sequences Recursive Rules Vocabulary: arithmetic sequence explicit form recursive form 4/11/2011
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Transcript of ©Evergreen Public Schools 2011 1 8.1 Arithmetic Sequences Recursive Rules Vocabulary : arithmetic...
©Evergreen Public Schools 2011
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8.1 Arithmetic SequencesRecursive Rules
Vocabulary:arithmetic sequenceexplicit formrecursive form
4/11/2011
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Practice 7. Look for and make use of structure.
Practice 8. Look for and express regularity in repeated reasoning.
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Sequences 3b I can write an arithmetic sequence in recursive form and translate between the explicit and recursive forms.
Sequences 2 I can write an equation and find specific terms of an arithmetic sequence in explicit form.
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LaunchLaunchLaunchLaunchYesterday, we completed the table
and wrote an equation to find the area of L(x) = 2x + 1
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LaunchLaunchLaunchLaunchWith arithmetic sequence L(x) = 2x + 1
• L(4) = 9. Find the term follows L(4)
• L(100) = 201. Find the term follows L(100)
• Find the term follows L(x)
• Find the term comes before L(x)
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Sequences from Unit 1Sequences from Unit 1
Seq Rule Rule
L(x) 3, 5, 7, …
L(x) = 2x + 1
k(x)17, 14, 11, …
k(x) =
We will learn this
today.
The rule in the 2nd column is called the explicit rule.
The rule in the 3rd column is called the recursive rule.
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How to Write the Recursive Rule
How to Write the Recursive Rule
L(x) = 3, 5, 7, …explicit equation: L(x) = 2x + 1In the pattern L(x) the next term is 2 more than what I have now.Now is L(x)Next is L(x+1)So rule is L(x+1) =
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How to Write a Recursive Rule
How to Write a Recursive Rule
a(x) = 7, 9, 11, … explicit rule: a(x) = 2x + 5The pattern in a is the next is 2 more than what I have now.Now is a(x)Next is a(x+1)So rule is a(x+1) = a(x) + 2 But wait, isn’t this the same rule for L?L(x+1) = L(x) + 2
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How to Write a Recursive Rule
How to Write a Recursive Rule
So the rule needs one more thing. What could that be?We need to know one term in the
sequence.L(x+1) = L(x) + 2 and L(1) = 3k(x+1) = a(x) – 3 and a(1) = 7
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How to Read a Recursive Rule
How to Read a Recursive Rule
For the sequenced(x+1)= d(x) – 5 and d(1) = 63• Find the first four terms in the
sequence. • If d(20) = -33, find d(21)
• Write the explicit rule
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Write a Recursive Rule with f(x)
Write a Recursive Rule with f(x)
What if I wanted to write the rule with L(x) or k(x) instead of L(x+1) or k(x+1) ?
L(x) = k(x) = L(x) and k(x) are what I have now.What other term do I need?I need what I had before.L(x – 1) or k(x – 1)?
L(x – 1) + 2 and L(1) = 3
k(x – 1) + 2 and a(1) = 5
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Write rules for each of the sequences.
Write rules for each of the sequences.
Sequence Explicit Rule f(x)
Recursive Rule f(x + 1)
f(x) add 3__, 4, 7, 10, 13,
f(x) = 3x + 1
f(x + 1) = f(x) +3 and f(1) = 4
g(x)8, 14, 20, 26, …
N(x) 34, 30, 26, 22, …
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Debra’s rulesDebra’s rules
What do you think of Debra’s rules?
Sequence f(x)
f(x) 4, 7, 10, 13, …
f(x) = f(x-1) + 3 and f(2) = 7
g(x)8, 14, 20, 26, …
g(x) = I(x-1) + 6and I(4) = 26
N(x) 34, 30, 26, 22, …
N(x) = N(x-1) – 4 and N(3) = 26
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Find the rate of change for each sequence.
Find the rate of change for each sequence.
f(x) f(x + 1) Rate of Change
L(x) = L(x-1) + 2and L(1) = 3
L(x+1) = L(x) + 2and L(1) = 3
f(x) = f(x-1) + 3 and f(1) = 4
f(x+1) = f(x) + 3and f(1) = 4
g(x) = g(x-1) + 6and g(1) = 8
g(x+1) = g(x) + 6and g(1) = 8
N(x) = N(x-1) – 4 and N(1) = 34
N(x+1) = N(x) – 4 and N(1) = 34
+2
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Common DifferenceCommon Difference
7, 11, 15, 19, 23The rate of change is called the
common difference, d in an arithmetic sequence.
Why do you think it is called that? The first term of an arithmetic
sequence, a1 = 24 and the common difference d = 9. What are the first 5 terms of the sequence?
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Did you hit the target?Sequences 3c I can write an
arithmetic sequence in recursive form and translate between the explicit and recursive forms.
Sequences 2a I can write an equation and find specific terms of an arithmetic sequence in explicit form.
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PracticePractice
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Placemat Placemat
Write a recursive rule for the sequence p(x)
4, 15, 26, 37, …
Name 1
Name 2
Name 3
Name 4
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