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Arithmetic Sequences

Algebraic SequenceA pattern of numbers with a constant difference between

terms.

Examples: 1, 5, 9, 13, 17

-7, -1, 5, 11, 17 21, 20, 19, 18, 17

Write the next two terms in the sequence…..

7, 13, 19, 25, ___, ___31 37

Write the next two terms in the sequence…..

14, 22, 30, 38, 46, ___, ___54 62

Write the next two terms in the sequence…..

3, 7, 11, 15, ___, ___19 23

Write the next three terms in the sequence…..

4, 9, 14, 19, ___, ___, ___24 29 34

Write the next four terms in the sequence…..

7, 12, 17, ___, ___, ___, ___22 27 32 37

Write the first five terms of the sequence represented….. Start at 3 and increase by 10

Start at 4 and increase by 5

Start at 6 and increase by 2

3, 13, 23, 33, 43

4, 9, 14, 19, 24

6, 8, 10, 12, 14

EXAMPLE 1Write an expression for the nth

term in the sequence 3, 5, 7, 9, 11, …?

Step 1: Construct a process chart showing the position and the corresponding term.

Position “0” 1 2 3 4 5 nTerm 3 5 7 9 1

1+2

+2

+2

+2

Determine the common difference (the change) of the terms.

STEP 2

Common Difference: 2

This is the coefficient of n.

2n

Reverse the pattern to find the “zero” term.

STEP 3

Position “0” 1 2 3 4 5 nTerm 3 51 7 9 1

1-2

Zero term: 1

Common Difference: 2

FINISHING IT OFF

Zero Term: 1

n +2 12n + 1

EXAMPLE 1Write an expression for the nth

term in the sequence 1, 4, 13, 16, 25, …?

Step 1: Construct a process chart showing the position and the corresponding term.

Position “0” 1 2 5 6 9 nTerm 131 4 16 25

3 9 3 9

Determine the common difference (the change) of the terms.

STEP 2

Common Difference: 3

This is the coefficient of n.

3n

Reverse the pattern to find the “zero” term.

STEP 3

Position “0” 1 2 5 6 9 nTerm 1 4-2 13 16 25

-3

Zero term: -2

Common Difference: 3

FINISHING IT OFF

Zero Term: 2

n -3 23n - 2

Let’s review! Write the first five terms of the sequence represented….. Start at 4 and increase by 3

4 7 10 13 16Now let’s make a table…

n

1 23 4 5

Write the first five terms of the sequence represented by…..

2n + 1 n

12345

357911

The nth term is the position in the sequence.

Now it’s your turn… Write the first five terms of the sequence

represented by…..

3n + 2 5n – 1Hint: Make a Table!!!

n n

12345

12345

58111417

49141924

Let’s analyze arithmetic sequences...How do we identify the nth term of each sequence?

7, 12, 17, 22, …..

The nth term is ANY position (number) in the sequence.

Let’s write an expression to identify the nth term

1. What is the common difference? 2. What is the zero term?

+5

+5

+5

52

2+

5n + 2- 5

Let’s write another expression…

7, 13, 19, 25, ….. n

7131925

1234

+6

+6

+6

6 1+

6n + 1

- 6

Let’s try another one…

3, 7, 11, 15, …..Hint: Make a Table!!!

n

Think / Write / Share:

1) What are the steps to continuing a sequence?

2) What are the steps to creating a table given an expression?

3) What are the steps to writing an expression to describe a sequence?

Exit Poll Which of the following tasks is most

difficult for you? Why?

1. Finding the next two terms in a sequence

2. Using an expression to find terms in a sequence

3. Writing the Algebraic Expression for a sequence