©Evergreen Public Schools 2011 1 Learning Target Target 12 Level 3 I can write an arithmetic...

©Evergreen Public Schools 2011

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Target 12 Level 3 I can write an arithmetic sequence in recursive form and translate between the explicit and recursive forms.

Target 12 Level 2 I can write an equation and find specific terms of an arithmetic sequence in explicit form. (Target 7, Level 3)


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LaunchLaunchLaunchLaunch1. Complete the table and write

an equation to find the area of L(x).


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LaunchLaunchLaunchLaunch2. With arithmetic sequence f(x),

• What term follows f(4)?

• What term follows f(100)?

• What term follows f(x)?

• What term comes before f(x)?


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Sequences from Unit 3Sequences from Unit 3

Read at L(x) and a(x).Write a rule for both boxes on the

bottom of the pages.Seq Rule (on left) Rule (on

right)

L(x)

a(x)


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Sequences from Unit 3Sequences from Unit 3

Seq Rule Rule

L(x)

a(x)

We will talk about this tomorrow.

The rule in the 2nd column is called the recursive rule.

The rule in the 3rd column is called the explicit rule.


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How to Write the Recursive Rule

How to Write the Recursive Rule

The pattern in L(x) is the next is 2 more than what I have now.

Now is L(x)Next is L(x+1)So rule is L(x+1) = L(x) + 2


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How to Write a Recursive Rule


The 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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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) = 3a(x+1) = a(x) + 2 and a(1) = 5


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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) = -37, find d(21)


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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 a(x) instead of L(x+1) or a(x+1) ?

L(x) = a(x) = L(x) and a(x) are what I have now.What other term do I need?I need what I had before.L(x – 1) or a(x – 1)?

L(x – 1) + 2 and L(1) = 3

a(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 Recursive Rule f(x)

Recursive Rule f(x + 1)

f(x) 4, 7, 10, 13, …

I(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

I(x)8, 14, 20, 26, …

I(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

I(x) = I(x-1) + 6and I(1) = 8

I(x+1) = I(x) + 6and I(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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53124

Did you hit the target?Target 12 Level 3 I can write an arithmetic sequence in

recursive form and translate between the explicit and recursive forms.

Target 12 Level 2 I can write an equation and find specific terms of an arithmetic sequence in explicit form. (Target 7, Level 3)


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PracticePractice

Arithmetic Sequences KUTAProblems #23 – 30.


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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

©Evergreen Public Schools 2011 1 Learning Target Target 12 Level 3 I can write an arithmetic...

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